Molecular dynamics simulations (MDS) require massive amounts of computation, and the inherent parallelism of the method makes it highly suitable for the use of both SIMD and MIMD parallel computers. An implementation of an MDS program for transputer arrays is presented, for the simulation of rigid polyatomic molecules. In contrast to many problems on MIMD computers, the main loss of efficiency does not arise from the time spent in communication between processors, but rather from certain extra calculation and addressing that is inevitable in the parallel decomposition of the problem, and from a slight load imbalance. In fact, MDS provides an excellent practical example of the ability of the transputer to communicate and calculate in parallel, with minimal degradation of the computation rate. The algorithm used is designed to be very general to enable the use of an arbitrary number of transputers and any geometry of boundary conditions. Some comments on how the program could be extended to handle flexible molecules are provided, along with very encouraging timing comparisons with the CRAY X-MP.