Recent interest in the extraction of fine detail from field seismograms has stimulated the search for numerical modeling procedures which can produce synthetic seismograms for complex subsurface geometries and for arbitrary source-receiver separations. Among the various techniques available for this purpose, the replacement of the two-dimensional wave equation by a suitable finite-difference representation offers distinct advantages. This approach is simple and may be readily implemented. It automatically accounts for the proper relative amplitudes of the various arrivals and includes the contributions of converted waves, Rayleigh waves, diffractions from faulted zones, and head waves.Two computational schemes have been examined. For the so-called 'homogeneous formulation,' the standard boundary conditions between media of different elastic properties must be satisfied explicitly. In the case of the alternate 'heterogeneous formulation', these elastic properties may be specified at each grid point of a finite-difference mesh, and the boundary conditions are satisfied implicitly. The proper simulation of the source requires special treatment for both cases.Synthetic seismograms computed for several models of exploration interest serve to illustrate how the technique may help the interpreter. The examples also illustrate various implementational aspects of the finite-difference approach, which involve such phenomena as grid dispersion, artificial reflections from the edge of the model, and choice of spatial and temporal sampling increments.