diff --git a/src/larktools/ebnf_grammar.py b/src/larktools/ebnf_grammar.py
index 8432ceb..7227a60 100644
--- a/src/larktools/ebnf_grammar.py
+++ b/src/larktools/ebnf_grammar.py
@@ -17,7 +17,9 @@
 
   assign_var: VARNAME "=" arith_expr 
 
+  variable: VARNAME ("[" INDEX "]")*
   VARNAME: LETTER (LETTER | DIGIT)*
+  INDEX: INT
 
   // Adopted from the calculator example at
   // https://lark-parser.readthedocs.io/en/stable/examples/calc.html 
@@ -33,7 +35,7 @@
   multiplication: product "*" atom
   division: product "/" atom
 
-  atom: INT | VARNAME | neg_atom | bracketed_arith_expr
+  atom: INT | variable | neg_atom | bracketed_arith_expr
   neg_atom: "-" atom
   bracketed_arith_expr: "(" arith_expr ")"
 
diff --git a/src/larktools/evaluation.py b/src/larktools/evaluation.py
index d480b68..eceec1c 100644
--- a/src/larktools/evaluation.py
+++ b/src/larktools/evaluation.py
@@ -85,9 +85,8 @@ def eval_atom(node, env):
     child_name = get_name(child)
     if child_name == "INT":
         return int(get_value(child))
-    elif child_name == "VARNAME":
-        varname = get_value(child)
-        return env[varname]
+    elif child_name == "variable":
+        return eval_variable(child, env)
     elif child_name == "neg_atom":
         return eval_neg_atom(child, env)
     elif child_name == "bracketed_arith_expr":
@@ -109,3 +108,16 @@ def eval_bracketed_arith_expr(node, env):
     child = get_children(node)[0]
     assert get_name(child) == "arith_expr"
     return eval_arith_expr(child, env)
+
+
+def eval_variable(node, env):
+    children = get_children(node)
+    assert get_name(children[0]) == "VARNAME"
+    varname = get_value(children[0])
+    value = env[varname]
+    if len(children) > 1:
+        for ch in children[1:]:
+            assert get_name(ch) == "INDEX"
+            idx = int(get_value(ch))
+            value = value[idx]
+    return value
diff --git a/tests/test_arithmetic.py b/tests/test_arithmetic.py
index 8ceda89..14bf12d 100644
--- a/tests/test_arithmetic.py
+++ b/tests/test_arithmetic.py
@@ -12,15 +12,15 @@ def __init__(self):
         self.parser = Lark(grammar, parser="lalr", start="arith_expr")
         self.parse = self.parser.parse
 
-    def parse_and_eval(self, expression: str, env: Optional[Union[None, dict]] = None) -> Union[int, float]:
+    def parse_and_eval(self, expression: str, env: Optional[dict] = None) -> Union[int, float]:
         tree = self.parse(expression)
         res = eval_arith_expr(tree, {} if env is None else env)
         return res
 
 
-def _parse_and_assert(expression: str, expected: Union[int, float]) -> None:
+def _parse_and_assert(expression: str, expected: Union[int, float], env: Optional[dict] = None) -> None:
     parser = ArithParser()
-    res = parser.parse_and_eval(expression)
+    res = parser.parse_and_eval(expression, env)
     assert expected == res
 
 def test_integer_addition():
@@ -38,3 +38,21 @@ def test_float_addition():
     _parse_and_assert("3.00000001 + 5.2", 8.20000001)
     _parse_and_assert("5e3 + 1.23E-2", 5000.00123)
 
+
+def test_simple_variable_evaluation():
+    _parse_and_assert("x", 10, {"x": 10})
+
+
+def test_array_variable_evaluation():
+    array = [i for i in range(5)]
+    _parse_and_assert("x[2]", 2, {"x": array})
+
+
+def test_nested_array_evaluation():
+    nested_array = [1, [2, 3], 4]
+    _parse_and_assert("x[1][0]", 2, {"x": nested_array})
+
+
+def test_nested_array_in_arith_expr():
+    nested_array = [1, [2, 3], 4]
+    _parse_and_assert("(x[1][0] + 2)/2", 2, {"x": nested_array})