The scattering and diffraction of plane seismic waves by two dimensional inhomogeneities have been studied. A least-squares technique has been employed to solve the problem. Two numerical methods have been proposed to avoid the Ill-conditioning in the resulting system of equations. Results are obtained using the series expansion in terms of Bessel and Hankel functions. Some known exact solutions are used to test the accuracy of this approximate method. The method is then applied to idealized cross sections along profiles of Los Angeles basin to investigate the effects of subsurface inhomogeneities on scattering and diffraction of plane SH, longitudinal P, and transverse SV waves. The surface displacement amplitudes and displacement amplitudes along buried horizontal lines are presented. Different angles of incidence and input frequencies are considered. For SV-wave excitation the incident angles below and beyond critical angle have been considered.; The study also includes an analysis of transient motions. The analysis is carried out using the transfer functions obtained from harmonic analysis. Three accelerograms from 1971 San Fernando earthquake are used to illustrate the effects of subsurface inhomogeneities upon transient motions. The results are presented in terms of amplitude spectra and accelerograms at several points on the surface of the inhomogeneity.