A method for the finite element computation of the synthetic seismograms of SH wave propagation in a two-dimensional (2-D) medium is proposed. The finite element method has the advantage of specifying the arbitrary density and velocity field in the medium. To complete the waveform modeling for an earthquake, the transformation of line source snapshots and seismograms of the 2-D finite element modeling to the point source responses is critically necessary. The accuracy of the finite element modeling is verified by comparing it with the generalized ray method and with a finite difference method which computes the 2-D wave field from a different approach. The aim of this study is to demonstrate the successfulness of seismogram synthesis by the finite element method and to propose the potential applications of this method in the Taiwan area.