Abstract: A less-costly numerical method is developed to obtain the theoretical seismograms at locations near a seismic source in an elastic half-space. An arbitrary shear dislocation point source is first considered as a linear combination of four basic ones, their combination coefficients are determined by the fault dip angle and slip direction. Each basic point source problem is then reduced to an axis-symmetric problem which is solved by the numerical method combining finite difference method and a new scheme dealing with the artificial boundary. By comparing the method of this paper with the present available analytical method, it can be concluded that the method of this paper consumes much less computer time for complicated near field problems.A set of near field theoretical seismograms for the basic dislocation point sources is presented and some features of near field ground motion, such as the horizontal displacements may be of about the same magsitude as the vertical ones and etc., are discussed.The numerical method of this paper can easily generalized to resolve problems of a finite shear dislocation source in a layered medium. Puthermore, it can be applied to study more complex near field wave propagation problems.