The spreading of a thin, planar drop of fluid that completely wets a solid surface is described, from an initial state in which the drop has a compact shape through its final approach to an infinitesimally thin film extending to infinity. Because the slope of the drop surface is everywhere small, the lubrication approximation can be used, and the effects of capillarity, viscosity, and intermolecular forces are all included. It is shown that a simple model for the intermolecular forces allows a mathematically acceptable solution to be found, without the need to invoke a large‐distance cutoff and without violating the small‐slope requirement of lubrication theory. ©1995 American Institute of Physics.