We present a new solver and interpolation algorithm for the theory of arrays with constant arrays. It is based on our previous work on weakly equivalent arrays. Constant arrays store the same value at every index, which is useful for model checking of programs with initialised memory. Instead of using a store chain to explicitly initialise the memory, using a constant array can considerably simplify the queries and thus reduce the solving and interpolation time. We show that only a few new rules are required for constant arrays and prove the correctness of the decision procedure and the interpolation procedure. We implemented the algorithm in our interpolating solver SMTInterpol.