diff --git a/xdsl_smt/dialects/smt_tensor_dialect.py b/xdsl_smt/dialects/smt_tensor_dialect.py
index eced1e75..3e1a7eb9 100644
--- a/xdsl_smt/dialects/smt_tensor_dialect.py
+++ b/xdsl_smt/dialects/smt_tensor_dialect.py
@@ -69,6 +69,8 @@ def get_element_type(self) -> AttributeCovT:
 
 
 AnySMTTensorType: TypeAlias = SMTTensorType[Attribute]
+INDEX_WIDTH = 64
+IndexType = BitVectorType(INDEX_WIDTH)
 
 
 def to_integer_array_attr(
diff --git a/xdsl_smt/passes/lower_smt_tensor.py b/xdsl_smt/passes/lower_smt_tensor.py
new file mode 100644
index 00000000..288e7090
--- /dev/null
+++ b/xdsl_smt/passes/lower_smt_tensor.py
@@ -0,0 +1,68 @@
+from xdsl_smt.dialects import smt_array_dialect as smt_array
+
+from xdsl_smt.dialects.smt_dialect import (
+    DeclareConstOp,
+)
+from xdsl_smt.dialects.smt_tensor_dialect import (
+    IndexType,
+    SMTTensorType,
+    TensorExtractOp,
+)
+from xdsl_smt.passes.dead_code_elimination import DeadCodeElimination
+from xdsl.dialects.builtin import ModuleOp
+from xdsl.ir import Attribute
+from xdsl.utils.hints import isa
+from xdsl.context import Context
+from xdsl.pattern_rewriter import (
+    GreedyRewritePatternApplier,
+    PatternRewriteWalker,
+    PatternRewriter,
+    RewritePattern,
+    op_type_rewrite_pattern,
+)
+from xdsl.passes import ModulePass
+
+
+def lower_tensor_type(typ: Attribute) -> Attribute:
+    if isa(typ, SMTTensorType):
+        result = typ.element_type
+        index_type = IndexType
+        for _ in typ.shape:
+            result = smt_array.ArrayType(index_type, result)
+        return result
+    return typ
+
+
+class DeclareConstOpPattern(RewritePattern):
+    @op_type_rewrite_pattern
+    def match_and_rewrite(self, op: DeclareConstOp, rewriter: PatternRewriter):
+        if isa(op.res.type, SMTTensorType):
+            new_constant_op = DeclareConstOp(lower_tensor_type(op.res.type))
+            rewriter.replace_matched_op(new_constant_op)
+
+
+class TensorExtractOpPattern(RewritePattern):
+    @op_type_rewrite_pattern
+    def match_and_rewrite(self, op: TensorExtractOp, rewriter: PatternRewriter):
+        source = op.tensor
+        assert isinstance(source.type, smt_array.ArrayType)
+        select_ops: list[smt_array.SelectOp] = []
+        for idx in op.indices:
+            select_ops.append(smt_array.SelectOp(source, idx))
+            source = select_ops[-1].res
+        rewriter.replace_matched_op(select_ops)
+
+
+class LowerSMTTensor(ModulePass):
+    name = "lower-smt-tensor"
+
+    def apply(self, ctx: Context, op: ModuleOp):
+        walker = PatternRewriteWalker(
+            GreedyRewritePatternApplier(
+                [DeclareConstOpPattern(), TensorExtractOpPattern()]
+            )
+        )
+        walker.rewrite_module(op)
+
+        # Apply DCE pass
+        DeadCodeElimination().apply(ctx, op)
diff --git a/xdsl_smt/passes/rewrite_smt_tensor.py b/xdsl_smt/passes/rewrite_smt_tensor.py
new file mode 100644
index 00000000..d761fac8
--- /dev/null
+++ b/xdsl_smt/passes/rewrite_smt_tensor.py
@@ -0,0 +1,83 @@
+from abc import ABC
+
+
+from xdsl_smt.dialects import smt_bitvector_dialect as smt_bv
+
+from xdsl.ir import SSAValue
+from xdsl_smt.dialects.smt_tensor_dialect import (
+    TensorTransposeOp,
+    INDEX_WIDTH,
+    TensorExtractOp,
+)
+from xdsl.dialects.builtin import ModuleOp
+from xdsl.context import Context
+from xdsl.pattern_rewriter import (
+    GreedyRewritePatternApplier,
+    PatternRewriteWalker,
+    PatternRewriter,
+    RewritePattern,
+    op_type_rewrite_pattern,
+)
+from xdsl.passes import ModulePass
+
+
+bv_constants: dict[int, smt_bv.ConstantOp] = {}
+
+
+def getBVConstant(x: int) -> smt_bv.ConstantOp:
+    global bv_constants
+    if x not in bv_constants:
+        bv_constants[x] = smt_bv.ConstantOp.from_int_value(x, INDEX_WIDTH)
+    return bv_constants[x]
+
+
+class TensorRewritePattern(RewritePattern, ABC):
+    extract_op: TensorExtractOp
+
+    def __init__(self, extract_op: TensorExtractOp):
+        self.extract_op = extract_op
+        super().__init__()
+
+
+class RewriteTransposeOpPattern(TensorRewritePattern):
+    @op_type_rewrite_pattern
+    def match_and_rewrite(self, op: TensorTransposeOp, rewriter: PatternRewriter):
+        extract_op = self.extract_op
+        permutations = op.get_permutation()
+        new_indices: list[SSAValue] = []
+        for i in permutations:
+            new_indices.append(extract_op.indices[i])
+        new_extract_op = TensorExtractOp(op.operand, new_indices)
+        rewriter.replace_op(extract_op, new_extract_op)
+        rewriter.erase_matched_op()
+
+
+class TensorExtractOpPattern(RewritePattern):
+    @op_type_rewrite_pattern
+    def match_and_rewrite(self, op: TensorExtractOp, rewriter: PatternRewriter):
+        source = op.tensor
+        source_parent_op = source.owner
+        if isinstance(source_parent_op, TensorTransposeOp):
+            RewriteTransposeOpPattern(op).match_and_rewrite(source_parent_op, rewriter)
+
+
+def insertConstantsBeforeModule(op: ModuleOp):
+    global bv_constants
+
+    block = op.body.block
+    first_op = block.first_op
+    assert first_op is not None
+    for val in bv_constants.values():
+        block.insert_op_before(val, first_op)
+
+
+class RewriteSMTTensor(ModulePass):
+    name = "rewrite-smt-tensor"
+
+    def apply(self, ctx: Context, op: ModuleOp):
+        walker = PatternRewriteWalker(
+            GreedyRewritePatternApplier([TensorExtractOpPattern()]), walk_reverse=True
+        )
+        walker.rewrite_module(op)
+
+        insertConstantsBeforeModule(op)