With Shih-Hsien Yu, we have studied the multi-dimensional wave propagation over a shock profile. There are rich wave phenomena resulting from the strong nonlinear nature of the shock wave and the dispersion of multi-dimensional waves. We start with the construction of the Green's function for the inviscid shock and then for the viscous profile. Exact algebraic manipulations on the level of Laplace-Fourier variables allow for explicit construction of the Green's function. New wave types are found through these exact computations. We apply our approach to a system motivated by the Euler equations in the gas dynamics.