An algorithm was developed for the simulation of 3-D elastodynamic wave propagation using displacement-stress relations. The parsimonious staggered grid scheme was adopted instead of the standard staggered grid scheme since it requires less computational memory. The double-couple point shear dislocation source was implemented into the numerical grid by using the moment tensor components as the body force couples. Anelastic attenuation was incorporated in the modelling by applying a simple attenuation function. Simulations of a half-space model for different grid sizes using a fixed amount of moment per unit volume are in accordance with the effective total moment used. Snapshots of a layered model reveal the accuracy and stability of the scheme at different discontinuities. The effect of soil velocity on amplitude amplification and increase in signal duration was studied and results depict increase in amplification and duration with decrease of velocity in the surficial layer. Further, it was found that horizontal components were more amplified as compared to the vertical component.