Pressure field contact (PFC) generalizes the flat Winkler elastic foundation model to contact situations with arbitrary, non-convex, coarsely meshed solid geometries. PFC calculates the deformed contact surface, the traction distribution on that surface, and, consequently, the net wrench (the net force and moment) between the objects. This model is useful in situations where deformation in the contact region is qualitatively important, but need not be accurate. PFC is a model of, and not a convergent approximation of, continuum mechanics. In PFC, each of the two contacting objects is assigned an immutable internal virtual `pressure' field. This continuous scalar field is zero on an undeformed object's outer boundaries and increases with depth. This pressure field is chosen to indirectly mimic physical properties such as (possibly spatially varying) elastic constants or a compliant layer's thickness. In regions where two rigid objects nominally overlap, the PFC contact surface is defined as the set of points where the two pressure fields are equal. This compliant unilateral contact model can add deformation details to otherwise rigid-object simulations.