Modeling the migration of spilled non-aqueous phase liquids (NAPLs) is currently difficult because the physics governing their movement is complex and knowledge of the local geology is always incomplete. NAPL movement is subject to buoyancy, capillary, and viscous forces in addition to being directed by the particular structural and hydraulic properties of the porous medium. Consideration of buoyancy forces suggests that the flow regime diagram of Lenormand et al. <1988> can be expanded to a third dimension. We develop a generalized growth model, based on invasion percolation, that captures the essential physics of initial NAPL migration but is simple enough computationally that simulations can be conducted much faster than by using continuum simulation models that attempt to capture all details of the physics. In comparison with available experimental data, our model realistically simulates movement of a NAPL for a wide range of values of Bond and capillary numbers, in any kind of porous medium. Because this approach allows much faster and simpler simulation than other approaches, a higher spatial resolution and/or the use of Monte Carlo methods to reduce the effect of geological uncertainty becomes a realistic possibility. ¿ 1998 American Geophysical Union