Model counting procedures for data structures are crucial for advancing the field of automated quantitative program analysis. We present a tool for Model Counting for Bounded Array Theory (MCBAT). MCBAT works on quantified integer array constraints in which all arrays have a finite length. We employ reductions from the theory of arrays to uninterpreted functions and linear integer arithmetic (LIA). Once reduced to LIA, we leverage Barvinok's polynomial time integer lattice point enumeration algorithm. Finally, we present a case study demonstrating applicability to automated quantitative program analysis. MCBAT is available for immediate use as a Docker image and the source code is freely available in our Github repository.