A particle-in-cell method, which has been successfully applied to problems in plasma physics, is adapted to the problem of oceanic geostrophic fronts. The thrust of the present article is the development, exposition, and testing of the method by means of synthetic examples. The advantage of this approach is its direct applicability to a class of oceanic problems which, for the most part, have remained unsolved. The method is computationally straightforward and efficient. It is also robust (the overall solution does not depend on the details of the initial distribution of material points) and numerically accurate (invariants are well conserved). ¿ American Geophysical Union 1988