The shell function method is presented as a new technique to evaluate the acoustic pressure field produced by a practical source of finite area, in a medium having an arbitrary spatially varying sound speed in three dimensions. Instead of initially subdividing the source surface area into many area elements, the shell function method determines the surface element of source area associated with the ray received at the observation point for a specified travel time. Special attention is given to the deficiency of conventional ray tracing for the case of a caustic, where an infinite pressure is predicted. On the other hand, the shell function method takes into account both the convergent state of a sound beam and the corresponding surface element of the source area. As a consequence, the sound pressure at and in the vicinity of caustics can be given an appropriate value directly. Numerical examples are included to show the computational procedure of the shell function method and the ensuing results.