Index: llvm/lib/Target/AMDGPU/AMDGPUInstructionSelector.cpp
===================================================================
--- llvm/lib/Target/AMDGPU/AMDGPUInstructionSelector.cpp
+++ llvm/lib/Target/AMDGPU/AMDGPUInstructionSelector.cpp
@@ -1964,6 +1964,12 @@
 
   std::tie(IdxBaseReg, Offset, Unused)
     = AMDGPU::getBaseWithConstantOffset(MRI, IdxReg);
+  if (IdxBaseReg == AMDGPU::NoRegister) {
+    // This will happen if the index is a known constant. This should ordinarily
+    // be legalized out, but handle it as a register just in case.
+    assert(Offset == 0);
+    IdxBaseReg = IdxReg;
+  }
 
   ArrayRef<int16_t> SubRegs = TRI.getRegSplitParts(SuperRC, EltSize);
 
Index: llvm/test/CodeGen/AMDGPU/GlobalISel/inst-select-extract-vector-elt.mir
===================================================================
--- llvm/test/CodeGen/AMDGPU/GlobalISel/inst-select-extract-vector-elt.mir
+++ llvm/test/CodeGen/AMDGPU/GlobalISel/inst-select-extract-vector-elt.mir
@@ -784,3 +784,58 @@
     %4:vgpr(s32) = G_EXTRACT_VECTOR_ELT %0, %3
     S_ENDPGM 0, implicit %4
 ...
+
+---
+name: extract_vector_elt_s_s32_v4s32_const_idx
+legalized: true
+regBankSelected: true
+
+body: |
+  bb.0:
+    liveins: $sgpr0_sgpr1_sgpr2_sgpr3
+
+    ; MOVREL-LABEL: name: extract_vector_elt_s_s32_v4s32_const_idx
+    ; MOVREL: [[COPY:%[0-9]+]]:sgpr_128 = COPY $sgpr0_sgpr1_sgpr2_sgpr3
+    ; MOVREL: [[S_MOV_B32_:%[0-9]+]]:sreg_32 = S_MOV_B32 0
+    ; MOVREL: $m0 = COPY [[S_MOV_B32_]]
+    ; MOVREL: [[S_MOVRELS_B32_:%[0-9]+]]:sreg_32 = S_MOVRELS_B32 [[COPY]].sub0, implicit $m0, implicit [[COPY]]
+    ; MOVREL: S_ENDPGM 0, implicit [[S_MOVRELS_B32_]]
+    ; GPRIDX-LABEL: name: extract_vector_elt_s_s32_v4s32_const_idx
+    ; GPRIDX: [[COPY:%[0-9]+]]:sgpr_128 = COPY $sgpr0_sgpr1_sgpr2_sgpr3
+    ; GPRIDX: [[S_MOV_B32_:%[0-9]+]]:sreg_32 = S_MOV_B32 0
+    ; GPRIDX: $m0 = COPY [[S_MOV_B32_]]
+    ; GPRIDX: [[S_MOVRELS_B32_:%[0-9]+]]:sreg_32 = S_MOVRELS_B32 [[COPY]].sub0, implicit $m0, implicit [[COPY]]
+    ; GPRIDX: S_ENDPGM 0, implicit [[S_MOVRELS_B32_]]
+    %0:sgpr(<4 x s32>) = COPY $sgpr0_sgpr1_sgpr2_sgpr3
+    %1:sgpr(s32) = G_CONSTANT i32 0
+    %2:sgpr(s32) = G_EXTRACT_VECTOR_ELT %0, %1
+    S_ENDPGM 0, implicit %2
+...
+
+---
+name: extract_vector_elt_v_s32_v4s32_const_idx
+legalized: true
+regBankSelected: true
+
+body: |
+  bb.0:
+    liveins: $vgpr0_vgpr1_vgpr2_vgpr3
+
+    ; MOVREL-LABEL: name: extract_vector_elt_v_s32_v4s32_const_idx
+    ; MOVREL: [[COPY:%[0-9]+]]:vreg_128 = COPY $sgpr0_sgpr1_sgpr2_sgpr3
+    ; MOVREL: [[S_MOV_B32_:%[0-9]+]]:sreg_32 = S_MOV_B32 0
+    ; MOVREL: $m0 = COPY [[S_MOV_B32_]]
+    ; MOVREL: [[V_MOVRELS_B32_e32_:%[0-9]+]]:vgpr_32 = V_MOVRELS_B32_e32 undef [[COPY]].sub0, implicit $m0, implicit $exec, implicit [[COPY]]
+    ; MOVREL: S_ENDPGM 0, implicit [[V_MOVRELS_B32_e32_]]
+    ; GPRIDX-LABEL: name: extract_vector_elt_v_s32_v4s32_const_idx
+    ; GPRIDX: [[COPY:%[0-9]+]]:vreg_128 = COPY $sgpr0_sgpr1_sgpr2_sgpr3
+    ; GPRIDX: [[S_MOV_B32_:%[0-9]+]]:sreg_32 = S_MOV_B32 0
+    ; GPRIDX: S_SET_GPR_IDX_ON [[S_MOV_B32_]], 1, implicit-def $m0, implicit $m0
+    ; GPRIDX: [[V_MOV_B32_e32_:%[0-9]+]]:vgpr_32 = V_MOV_B32_e32 undef [[COPY]].sub0, implicit $exec, implicit [[COPY]], implicit $m0
+    ; GPRIDX: S_SET_GPR_IDX_OFF
+    ; GPRIDX: S_ENDPGM 0, implicit [[V_MOV_B32_e32_]]
+    %0:vgpr(<4 x s32>) = COPY $sgpr0_sgpr1_sgpr2_sgpr3
+    %1:sgpr(s32) = G_CONSTANT i32 0
+    %2:vgpr(s32) = G_EXTRACT_VECTOR_ELT %0, %1
+    S_ENDPGM 0, implicit %2
+...
Index: llvm/test/CodeGen/AMDGPU/GlobalISel/inst-select-insert-vector-elt.mir
===================================================================
--- llvm/test/CodeGen/AMDGPU/GlobalISel/inst-select-insert-vector-elt.mir
+++ llvm/test/CodeGen/AMDGPU/GlobalISel/inst-select-insert-vector-elt.mir
@@ -624,3 +624,66 @@
     %5:sgpr(<8 x s32>) = G_INSERT_VECTOR_ELT %0, %1, %4
     S_ENDPGM 0, implicit %5
 ...
+
+# This should have been folded out in the legalizer, but make sure it
+# doesn't crash.
+---
+name: insert_vector_elt_s_s32_v4s32_const_idx
+legalized: true
+regBankSelected: true
+
+body: |
+  bb.0:
+    liveins: $sgpr0_sgpr1_sgpr2_sgpr3, $sgpr4
+
+    ; MOVREL-LABEL: name: insert_vector_elt_s_s32_v4s32_const_idx
+    ; MOVREL: [[COPY:%[0-9]+]]:sgpr_128 = COPY $sgpr0_sgpr1_sgpr2_sgpr3
+    ; MOVREL: [[COPY1:%[0-9]+]]:sreg_32 = COPY $sgpr4
+    ; MOVREL: [[S_MOV_B32_:%[0-9]+]]:sreg_32 = S_MOV_B32 0
+    ; MOVREL: $m0 = COPY [[S_MOV_B32_]]
+    ; MOVREL: [[S_INDIRECT_REG_WRITE_B32_V4_:%[0-9]+]]:sgpr_128 = S_INDIRECT_REG_WRITE_B32_V4 [[COPY]], [[COPY1]], 1, implicit $m0
+    ; MOVREL: S_ENDPGM 0, implicit [[S_INDIRECT_REG_WRITE_B32_V4_]]
+    ; GPRIDX-LABEL: name: insert_vector_elt_s_s32_v4s32_const_idx
+    ; GPRIDX: [[COPY:%[0-9]+]]:sgpr_128 = COPY $sgpr0_sgpr1_sgpr2_sgpr3
+    ; GPRIDX: [[COPY1:%[0-9]+]]:sreg_32 = COPY $sgpr4
+    ; GPRIDX: [[S_MOV_B32_:%[0-9]+]]:sreg_32 = S_MOV_B32 0
+    ; GPRIDX: $m0 = COPY [[S_MOV_B32_]]
+    ; GPRIDX: [[S_INDIRECT_REG_WRITE_B32_V4_:%[0-9]+]]:sgpr_128 = S_INDIRECT_REG_WRITE_B32_V4 [[COPY]], [[COPY1]], 1, implicit $m0
+    ; GPRIDX: S_ENDPGM 0, implicit [[S_INDIRECT_REG_WRITE_B32_V4_]]
+    %0:sgpr(<4 x s32>) = COPY $sgpr0_sgpr1_sgpr2_sgpr3
+    %1:sgpr(s32) = COPY $sgpr4
+    %2:sgpr(s32) = G_CONSTANT i32 0
+    %3:sgpr(<4 x s32>) = G_INSERT_VECTOR_ELT %0, %1, %2
+    S_ENDPGM 0, implicit %3
+...
+
+---
+name: insert_vector_elt_v_s32_v4s32_const_idx
+legalized: true
+regBankSelected: true
+
+body: |
+  bb.0:
+    liveins: $sgpr0_sgpr1_sgpr2_sgpr3, $sgpr4
+
+    ; MOVREL-LABEL: name: insert_vector_elt_v_s32_v4s32_const_idx
+    ; MOVREL: [[COPY:%[0-9]+]]:vreg_128 = COPY $sgpr0_sgpr1_sgpr2_sgpr3
+    ; MOVREL: [[COPY1:%[0-9]+]]:sreg_32 = COPY $sgpr4
+    ; MOVREL: [[S_MOV_B32_:%[0-9]+]]:sreg_32 = S_MOV_B32 0
+    ; MOVREL: $m0 = COPY [[S_MOV_B32_]]
+    ; MOVREL: [[V_INDIRECT_REG_WRITE_B32_V4_:%[0-9]+]]:vreg_128 = V_INDIRECT_REG_WRITE_B32_V4 [[COPY]], [[COPY1]], 1, implicit $m0, implicit $exec
+    ; MOVREL: S_ENDPGM 0, implicit [[V_INDIRECT_REG_WRITE_B32_V4_]]
+    ; GPRIDX-LABEL: name: insert_vector_elt_v_s32_v4s32_const_idx
+    ; GPRIDX: [[COPY:%[0-9]+]]:vreg_128 = COPY $sgpr0_sgpr1_sgpr2_sgpr3
+    ; GPRIDX: [[COPY1:%[0-9]+]]:sreg_32 = COPY $sgpr4
+    ; GPRIDX: [[S_MOV_B32_:%[0-9]+]]:sreg_32 = S_MOV_B32 0
+    ; GPRIDX: S_SET_GPR_IDX_ON [[S_MOV_B32_]], 8, implicit-def $m0, implicit $m0
+    ; GPRIDX: [[V_INDIRECT_REG_WRITE_B32_V4_:%[0-9]+]]:vreg_128 = V_INDIRECT_REG_WRITE_B32_V4 [[COPY]], [[COPY1]], 1, implicit $m0, implicit $exec
+    ; GPRIDX: S_SET_GPR_IDX_OFF
+    ; GPRIDX: S_ENDPGM 0, implicit [[V_INDIRECT_REG_WRITE_B32_V4_]]
+    %0:vgpr(<4 x s32>) = COPY $sgpr0_sgpr1_sgpr2_sgpr3
+    %1:sgpr(s32) = COPY $sgpr4
+    %2:sgpr(s32) = G_CONSTANT i32 0
+    %3:vgpr(<4 x s32>) = G_INSERT_VECTOR_ELT %0, %1, %2
+    S_ENDPGM 0, implicit %3
+...