Abstract: Numerical calculations have been made for the backscattering of acoustic pulse waves from a spherical scatterer in a solid using the exact theory of Ying et al. and FFT technique. A ray tracing-diffraction theory has been presented based on the ray tracing theory in optics and taking diffraction into account to deal with the back-scattering of pulse waves （both longitudinal and shear） from an odd shaped scatterer with no sharp corner on the surface in a solid. The results are in good agreement with the exact theory in the case of a spherical scatterer. As an example, the backs-catterings of longitudinal as well as shear waves from an elliptical void and WC inclusion in Si₃N₄ are shown.