Index: mlir/lib/Dialect/Arith/IR/ArithOps.cpp
===================================================================
--- mlir/lib/Dialect/Arith/IR/ArithOps.cpp
+++ mlir/lib/Dialect/Arith/IR/ArithOps.cpp
@@ -13,6 +13,7 @@
 
 #include "mlir/Dialect/Arith/IR/Arith.h"
 #include "mlir/Dialect/CommonFolders.h"
+#include "mlir/Dialect/UB/IR/UBOps.h"
 #include "mlir/IR/Builders.h"
 #include "mlir/IR/BuiltinAttributeInterfaces.h"
 #include "mlir/IR/BuiltinAttributes.h"
@@ -2184,6 +2185,13 @@
   if (trueVal == falseVal)
     return trueVal;
 
+  // If either operand is fully poisoned, return the other.
+  if (isa_and_nonnull<ub::PoisonAttr>(adaptor.getTrueValue()))
+    return falseVal;
+
+  if (isa_and_nonnull<ub::PoisonAttr>(adaptor.getFalseValue()))
+    return trueVal;
+
   Value condition = getCondition();
 
   // select true, %0, %1 => %0
Index: mlir/lib/Dialect/Arith/IR/CMakeLists.txt
===================================================================
--- mlir/lib/Dialect/Arith/IR/CMakeLists.txt
+++ mlir/lib/Dialect/Arith/IR/CMakeLists.txt
@@ -28,6 +28,7 @@
   MLIRInferIntRangeInterface
   MLIRInferTypeOpInterface
   MLIRIR
+  MLIRUBDialect
   )
 
 add_mlir_dialect_library(MLIRArithValueBoundsOpInterfaceImpl
Index: mlir/test/Dialect/Arith/canonicalize.mlir
===================================================================
--- mlir/test/Dialect/Arith/canonicalize.mlir
+++ mlir/test/Dialect/Arith/canonicalize.mlir
@@ -2567,3 +2567,13 @@
   %2 = arith.ori %arg0, %1 : index
   return %2 : index
 }
+
+// CHECK-LABEL: @selectOfPoison
+// CHECK-SAME: %[[ARG:[[:alnum:]]+]]: i32
+// CHECK: return %[[ARG]], %[[ARG]]
+func.func @selectOfPoison(%cond : i1, %arg: i32) -> (i32, i32) {
+  %poison = ub.poison : i32
+  %select1 = arith.select %cond, %poison, %arg : i32
+  %select2 = arith.select %cond, %arg, %poison : i32
+  return %select1, %select2 : i32, i32
+}
\ No newline at end of file