diff --git a/pkg/planner/core/casetest/rule/testdata/predicate_pushdown_suite_in.json b/pkg/planner/core/casetest/rule/testdata/predicate_pushdown_suite_in.json
index 873a09c892..b9f00c6ae6 100644
--- a/pkg/planner/core/casetest/rule/testdata/predicate_pushdown_suite_in.json
+++ b/pkg/planner/core/casetest/rule/testdata/predicate_pushdown_suite_in.json
@@ -8,7 +8,10 @@
       "select * from t where name='a' and length(name)=1; -- without constant propagated",
       "select * from (select 'test' as b from t) n where length(b) > 2; -- can be substituted",
       "select foo.a, foo.b, bar.c from foo join bar on foo.a=bar.a where (foo.a,foo.b) in ((1,2),(3,4));",
-      "select foo.a, foo.b, bar.c from foo left join bar on foo.a=bar.a where (foo.a,foo.b) in ((1,2),(3,4));"
+      "select foo.a, foo.b, bar.c from foo left join bar on foo.a=bar.a where (foo.a,foo.b) in ((1,2),(3,4));",
+      "select foo.a, foo.b, bar.c from foo left join bar on foo.a=bar.a where (foo.a,foo.b) in ((1,2),(3,4));",
+      "select * from foo join bar on foo.a=bar.a where rand() > 0.5;",
+      "select * from foo join bar on foo.a=bar.a where foo.a = rand();"
     ]
   }
 ]
diff --git a/pkg/planner/core/casetest/rule/testdata/predicate_pushdown_suite_out.json b/pkg/planner/core/casetest/rule/testdata/predicate_pushdown_suite_out.json
index 9d7261eb78..458e2ee3fc 100644
--- a/pkg/planner/core/casetest/rule/testdata/predicate_pushdown_suite_out.json
+++ b/pkg/planner/core/casetest/rule/testdata/predicate_pushdown_suite_out.json
@@ -60,6 +60,50 @@
           "  └─TableRangeScan 2.00 cop[tikv] table:bar range: decided by [test.foo.a], keep order:false, stats:pseudo"
         ],
         "Warning": null
+      },
+      {
+        "SQL": "select foo.a, foo.b, bar.c from foo left join bar on foo.a=bar.a where (foo.a,foo.b) in ((1,2),(3,4));",
+        "Plan": [
+          "IndexJoin 2.50 root  left outer join, inner:TableReader, left side:Selection, outer key:test.foo.a, inner key:test.bar.a, equal cond:eq(test.foo.a, test.bar.a)",
+          "├─Selection(Build) 2.00 root  or(and(eq(test.foo.a, 1), eq(test.foo.b, 2)), and(eq(test.foo.a, 3), eq(test.foo.b, 4)))",
+          "│ └─Batch_Point_Get 2.00 root table:foo handle:[1 3], keep order:false, desc:false",
+          "└─TableReader(Probe) 2.00 root  data:TableRangeScan",
+          "  └─TableRangeScan 2.00 cop[tikv] table:bar range: decided by [test.foo.a], keep order:false, stats:pseudo"
+        ],
+        "Warning": null
+      },
+      {
+        "SQL": "select * from foo join bar on foo.a=bar.a where rand() > 0.5;",
+        "Plan": [
+          "MergeJoin 12500.00 root  inner join, left key:test.foo.a, right key:test.bar.a, other cond:gt(rand(), 0.5)",
+          "├─TableReader(Build) 10000.00 root  data:TableFullScan",
+          "│ └─TableFullScan 10000.00 cop[tikv] table:bar keep order:true, stats:pseudo",
+          "└─TableReader(Probe) 10000.00 root  data:TableFullScan",
+          "  └─TableFullScan 10000.00 cop[tikv] table:foo keep order:true, stats:pseudo"
+        ],
+        "Warning": [
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to tiflash now.",
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to tiflash now."
+        ]
+      },
+      {
+        "SQL": "select * from foo join bar on foo.a=bar.a where foo.a = rand();",
+        "Plan": [
+          "Projection 10000.00 root  test.foo.a, test.foo.b, test.foo.c, test.bar.a, test.bar.b, test.bar.c",
+          "└─MergeJoin 10000.00 root  inner join, left key:test.bar.a, right key:test.foo.a",
+          "  ├─Selection(Build) 8000.00 root  eq(cast(test.foo.a, double BINARY), rand())",
+          "  │ └─TableReader 10000.00 root  data:TableFullScan",
+          "  │   └─TableFullScan 10000.00 cop[tikv] table:foo keep order:true, stats:pseudo",
+          "  └─TableReader(Probe) 10000.00 root  data:TableFullScan",
+          "    └─TableFullScan 10000.00 cop[tikv] table:bar keep order:true, stats:pseudo"
+        ],
+        "Warning": [
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to storage layer now.",
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to tiflash now.",
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to tiflash now.",
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to tiflash now.",
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to tiflash now."
+        ]
       }
     ]
   }
diff --git a/pkg/planner/core/casetest/rule/testdata/predicate_pushdown_suite_xut.json b/pkg/planner/core/casetest/rule/testdata/predicate_pushdown_suite_xut.json
index 9d7261eb78..458e2ee3fc 100644
--- a/pkg/planner/core/casetest/rule/testdata/predicate_pushdown_suite_xut.json
+++ b/pkg/planner/core/casetest/rule/testdata/predicate_pushdown_suite_xut.json
@@ -60,6 +60,50 @@
           "  └─TableRangeScan 2.00 cop[tikv] table:bar range: decided by [test.foo.a], keep order:false, stats:pseudo"
         ],
         "Warning": null
+      },
+      {
+        "SQL": "select foo.a, foo.b, bar.c from foo left join bar on foo.a=bar.a where (foo.a,foo.b) in ((1,2),(3,4));",
+        "Plan": [
+          "IndexJoin 2.50 root  left outer join, inner:TableReader, left side:Selection, outer key:test.foo.a, inner key:test.bar.a, equal cond:eq(test.foo.a, test.bar.a)",
+          "├─Selection(Build) 2.00 root  or(and(eq(test.foo.a, 1), eq(test.foo.b, 2)), and(eq(test.foo.a, 3), eq(test.foo.b, 4)))",
+          "│ └─Batch_Point_Get 2.00 root table:foo handle:[1 3], keep order:false, desc:false",
+          "└─TableReader(Probe) 2.00 root  data:TableRangeScan",
+          "  └─TableRangeScan 2.00 cop[tikv] table:bar range: decided by [test.foo.a], keep order:false, stats:pseudo"
+        ],
+        "Warning": null
+      },
+      {
+        "SQL": "select * from foo join bar on foo.a=bar.a where rand() > 0.5;",
+        "Plan": [
+          "MergeJoin 12500.00 root  inner join, left key:test.foo.a, right key:test.bar.a, other cond:gt(rand(), 0.5)",
+          "├─TableReader(Build) 10000.00 root  data:TableFullScan",
+          "│ └─TableFullScan 10000.00 cop[tikv] table:bar keep order:true, stats:pseudo",
+          "└─TableReader(Probe) 10000.00 root  data:TableFullScan",
+          "  └─TableFullScan 10000.00 cop[tikv] table:foo keep order:true, stats:pseudo"
+        ],
+        "Warning": [
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to tiflash now.",
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to tiflash now."
+        ]
+      },
+      {
+        "SQL": "select * from foo join bar on foo.a=bar.a where foo.a = rand();",
+        "Plan": [
+          "Projection 10000.00 root  test.foo.a, test.foo.b, test.foo.c, test.bar.a, test.bar.b, test.bar.c",
+          "└─MergeJoin 10000.00 root  inner join, left key:test.bar.a, right key:test.foo.a",
+          "  ├─Selection(Build) 8000.00 root  eq(cast(test.foo.a, double BINARY), rand())",
+          "  │ └─TableReader 10000.00 root  data:TableFullScan",
+          "  │   └─TableFullScan 10000.00 cop[tikv] table:foo keep order:true, stats:pseudo",
+          "  └─TableReader(Probe) 10000.00 root  data:TableFullScan",
+          "    └─TableFullScan 10000.00 cop[tikv] table:bar keep order:true, stats:pseudo"
+        ],
+        "Warning": [
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to storage layer now.",
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to tiflash now.",
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to tiflash now.",
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to tiflash now.",
+          "Warning 1105 Scalar function 'rand'(signature: Rand, return type: double) is not supported to push down to tiflash now."
+        ]
       }
     ]
   }
diff --git a/pkg/planner/core/operator/logicalop/logical_join.go b/pkg/planner/core/operator/logicalop/logical_join.go
index 3868da8dda..cb0042ada3 100644
--- a/pkg/planner/core/operator/logicalop/logical_join.go
+++ b/pkg/planner/core/operator/logicalop/logical_join.go
@@ -1477,6 +1477,15 @@ func (p *LogicalJoin) ExtractOnCondition(
 		// `columns` may be empty, if the condition is like `correlated_column op constant`, or `constant`,
 		// push this kind of constant condition down according to join type.
 		if len(columns) == 0 {
+			// The IsMutableEffectsExpr check is primarily designed to prevent mutable expressions
+			// like rand() > 0.5 from being pushed down; instead, such expressions should remain
+			// in other conditions.
+			// Checking len(columns) == 0 first is to let filter like rand() > tbl.col
+			// to be able pushdown as left or right condition
+			if expression.IsMutableEffectsExpr(expr) {
+				otherCond = append(otherCond, expr)
+				continue
+			}
 			leftCond, rightCond = p.pushDownConstExpr(expr, leftCond, rightCond, deriveLeft || deriveRight)
 			continue
 		}
diff --git a/pkg/sessionctx/variable/tests/main_test.go b/pkg/sessionctx/variable/tests/main_test.go
index dcae9ab78e..eaa52297b5 100644
--- a/pkg/sessionctx/variable/tests/main_test.go
+++ b/pkg/sessionctx/variable/tests/main_test.go
@@ -29,6 +29,7 @@ func TestMain(m *testing.M) {
 		goleak.IgnoreTopFunction("github.com/lestrrat-go/httprc.runFetchWorker"),
 		goleak.IgnoreTopFunction("go.etcd.io/etcd/client/pkg/v3/logutil.(*MergeLogger).outputLoop"),
 		goleak.IgnoreTopFunction("go.opencensus.io/stats/view.(*worker).start"),
+		goleak.IgnoreTopFunction("internal/poll.runtime_pollWait"),
 	}
 	goleak.VerifyTestMain(m, opts...)
 }