The realistic interpretation of seismic travel-time data from structurally complex areas, and the accurate location of earthquake hypocenters in such areas, require seismic ray computations for laterally inhomogeneous velocity models. Numerical simulation of the ray differential equations provides a practical means of performing the necessary calculations. A least-squares scheme is used to obtain models which fit travel-time data and are consistent with geological data. Laterally inhomogeneous velocity models are obtained for travel-time data from explosions for two areas in California: the Bear Valley area, 40 km southeast of Hollister and the Borrego Mountain area, 160 km northeast of San Diego. Both regions are characterized by a substantial lateral variation of seismic velocity, and the derived models exhibit most of the significant structural features of the areas. An algorithm for the direct solution of ray boundary value problems, based on the iterative solution of a tridiagonal set of simultaneous equations, allows for the input of geophysical intuition in finding the rays between a source and a station.