The responses of soft tissue under acoustic radiation force excitations are used to image tissue mechanical properties for soft tissue discrimination and detection of breast tumors. The soft tissue viscoelasticy has been interrogated by step acoustic radiation force excitations. The corresponding induced timedependent creep displacement is used to reconstruct soft tissue viscoelasticity or to estimate viscosity and elasticity contrast of the inclusion to background. The acoustic radiation force is highly localized in a small excitation region; and, one degreeof- freedom and homogenous assumptions are generally made to the analysis. However, these simplifying assumptions limit the accuracy of these methods. In this paper, a finite element model was built to demonstrate the effect of the dynamic response of viscoelastic heterogeneous soft tissue to step acoustic radiation force. Factors affecting the dynamic response of soft tissue were first investigated with the homogenous model, and the corresponding estimation quality based on the one degree-offreedom model was evaluated. Then, the dynamic response of soft tissue with inclusion and different elasticity and viscocity for the tissue and the inclusion was studied. The results suggest that in order to improve the estimate of soft tissue viscoelasticity the heterogenenous nature of the tissue and its three dimensional geometry should be accounted in the model.