Abstract: The solution of dynamic response of foundation is of great significance for a better understanding of the structure-soil interaction. However, the previous studies have mainly solved the frequency-domain solution for the isotropic layered soil, and few reports have been presented on the transverse isotropic layered soil, especially the solution in time domain. In the study, the dynamic response solution for the arbitrarily shaped foundation resting on (or) embedded in transversely isotropic multi-layered soil in time domain is obtained by using the integral transformation method, mixed variable technique and modified subtraction model. Numerical examples verify the accuracy of the proposed algorithm. Then a parameter study is carried out to analyze the influences of the difference between the material parameters in horizontal and vertical directions on the dynamic response of foundation in time domain. The results show that the heterogeneity of the soil has a significant effect on the dynamic response of the foundation, which should be considered in practical projects to obtain more accurate results.