A simple method is described for molecular dynamics simulation of fluids of nonspherical molecules on vector processing supercomputers such as the IBM-3090 with Vector Facility and the CRAY-XMP. Speeds-up of around two are reported for fluids modeled using a Gaussian overlap pair potential, a diatomic Lennard-Jones pair potential, and a six-site Lennard-Jones potential for benzene. It is also shown that modifications to make the program suitable for vector processing requires 5 to 10% more computation.