Fast estimation of point-source parameters for earthquakes has progressed much in recent years due to the development of broadband seismic networks. The expansion of these networks now provides the opportunity to investigate second-order effects such as source finiteness for regional and local events on a routine basis. This potential motivates the development of methods to quickly generate synthetic seismograms for finite sources. This is possible when the fault dimension is small compared to the source-receiver distance and when the structure around the source region is relatively simple. To study the directivity for a finite source, we discretize the fault region into a set of elements represented as point sources. We then generate the generalized rays for the best-fitting point-source location and derive for each separate ray the response for neighboring point sources using power series expansions. The response for a finite fault is then a summation over rays and elements. If we sum over elements first, we obtain an effective far-field source-time function for each ray, which is sensitive to the direction of rupture. These far-field source-time functions are convolved with the corresponding rays, and the results are summed to form the total response. A simple application of the above method is demonstrated with the tangential motions observed from the 1991 Sierra Madre earthquake. For this event, we constrain the fault dimension to be about 3 km with rupture toward the west, which is compatible with other more detailed studies.