In this work we present a replicated data hybrid OpenMP/MPI implementation of a hierarchical progression of approximate classical polarizable models that yields speedups of up to similar to 10 compared to the standard OpenMP implementation of the exact parent AMOEBA polarizable model. In addition, our parallel implementation exhibits reasonable weak and strong scaling. The resulting parallel software will prove useful for those who are interested in how molecular properties converge in the condensed phase with respect to the MBE, it provides a fruitful test bed for exploring different electrostatic embedding schemes, and offers an interesting possibility for future exascale computing paradigms. (C) 2016 Elsevier B.V. All rights reserved.