Molecular dynamics simulations require supercomputers. A specific class of supercomputers is that of parallel computers. We derive an implementation of molecular dynamics on a toroidal network of processors. First, we argue that for a fast algorithm the simulation universe has to be divided into regular cells, and we determine the best shape of these cells. For a parallel implementation, we choose to distribute cells rather than particles and we show how to assign the cells to processors, given certain restrictions on universe and network. The assignment is proven to be optimal with respect to communication cost. We go on to explain our implementation. Finally, we compare the timing results with those for computations performed on a Cray single-processor machine. The physical results obtained with the implementation are discussed elsewhere.