Index: mlir/lib/Dialect/LLVMIR/IR/LLVMDialect.cpp
===================================================================
--- mlir/lib/Dialect/LLVMIR/IR/LLVMDialect.cpp
+++ mlir/lib/Dialect/LLVMIR/IR/LLVMDialect.cpp
@@ -501,17 +501,15 @@
     // Extract the constant value from the operand and put it into the attribute
     // instead.
     APInt staticIndexValue;
-    bool matched =
-        matchPattern(indices[operandPos], m_ConstantInt(&staticIndexValue));
-    (void)matched;
-    assert(matched && "index into a struct must be a constant");
-    assert(staticIndexValue.sge(APInt::getSignedMinValue(/*numBits=*/32)) &&
-           "struct index underflows 32-bit integer");
-    assert(staticIndexValue.sle(APInt::getSignedMaxValue(/*numBits=*/32)) &&
-           "struct index overflows 32-bit integer");
-    auto staticIndex = static_cast<int32_t>(staticIndexValue.getSExtValue());
-    updatedStructIndices[pos] = staticIndex;
-    operandsToErase.push_back(operandPos);
+    if (matchPattern(indices[operandPos], m_ConstantInt(&staticIndexValue))) {
+      assert(staticIndexValue.sge(APInt::getSignedMinValue(/*numBits=*/32)) &&
+             "struct index underflows 32-bit integer");
+      assert(staticIndexValue.sle(APInt::getSignedMaxValue(/*numBits=*/32)) &&
+             "struct index overflows 32-bit integer");
+      auto staticIndex = static_cast<int32_t>(staticIndexValue.getSExtValue());
+      updatedStructIndices[pos] = staticIndex;
+      operandsToErase.push_back(operandPos);
+    }
   }
 
   for (unsigned i = 0, e = indices.size(); i < e; ++i) {
@@ -591,9 +589,13 @@
       continue;
 
     int32_t staticIndex = structIndices.getValues<int32_t>()[index];
+    // `findKnownStructIndices` merely tells you `index` _might_ be
+    // a struct index. So it's totally possible that `staticIndex`
+    // is still dynamic.
+    // FIXME: We probably should use LLVM's way to verify GEP indices,
+    // which recursively goes down the type heirarchy to perform the checks.
     if (staticIndex == LLVM::GEPOp::kDynamicIndex)
-      return emitOpError() << "expected index " << index
-                           << " indexing a struct to be constant";
+      continue;
     if (staticIndex < 0 || static_cast<unsigned>(staticIndex) >= structSizes[i])
       return emitOpError() << "index " << index
                            << " indexing a struct is out of bounds";
Index: mlir/lib/Target/LLVMIR/ConvertFromLLVMIR.cpp
===================================================================
--- mlir/lib/Target/LLVMIR/ConvertFromLLVMIR.cpp
+++ mlir/lib/Target/LLVMIR/ConvertFromLLVMIR.cpp
@@ -1012,7 +1012,8 @@
          llvm::enumerate(llvm::drop_begin(gep->operand_values()))) {
       llvm::Value *operand = en.value();
       if (llvm::find(staticIndexPositions, en.index()) ==
-          staticIndexPositions.end()) {
+              staticIndexPositions.end() ||
+          !isa<llvm::ConstantInt>(operand)) {
         staticIndices.push_back(GEPOp::kDynamicIndex);
         dynamicIndices.push_back(processValue(operand));
         if (!dynamicIndices.back())
Index: mlir/test/Target/LLVMIR/Import/verify-gep.ll
===================================================================
--- /dev/null
+++ mlir/test/Target/LLVMIR/Import/verify-gep.ll
@@ -0,0 +1,10 @@
+; RUN: mlir-translate --import-llvm %s | FileCheck %s
+
+%sub_struct = type { i32, i8 }
+%my_struct = type { %sub_struct, [4 x i32] }
+
+define void @foo(%my_struct* %arg, i32 %idx) {
+  ; CHECK: llvm.getelementptr %arg0
+  %1 = getelementptr %my_struct, %my_struct* %arg, i32 0, i32 1, i32 %idx
+  ret void
+}