This paper describes a vectorized and parallelized implementation of a two-dimensional pseudo-spectral seismic elastic model and of a (frequency-domain)seismic migration algorithm on the (tightly-coupled) vector multiprocessor IBM 3090 VF. Performance data of alternative parallel implementations on an LCAP (loosely coupled system of array processors FPS 164) are also given. The paper reports additionally performance data of a vector/parallel implementation on the IBM 3090 of some characteristic seismic velocity estimation algorithms. The three problems chosen are representative of a wide class of geophysical computations and the results summarized in this paper show their suitability to efficient implementation on the IBM 3090 vector multiprocessor: combined vector/parallel speedups in the range 15-30 are in fact observed. © 1989 Kluwer Academic Publishers.