Abstract: From fundamental theory of seismic wave propagation in stratified media, with reference to the techniques and applications already developed for calculating point-source-caused ground motion using generalized reflection and transmission matrices method, and with consideration of arbitrary geometry and tempo-spatially variable focal mechanisms of finite sources, as well as development trend of parallel computation, we improved computing-flow in the point-source case and developed a new program, GRTMatSyn, to be suitable for both point sources and finite sources with arbitrary geometries and tempo-spatially variable mechanisms. Numerical tests were carried out with necessary models of finite sources and observation points for reliability and computing efficiency of the application. The results were compared with those from CompSyn, a widely recognized program for calculating ground motion caused by a finite plane fault. The comparison indicated that the application developed in this study is reliable and rather more efficient.