In this third article of a series study attempting to present a new method of seismogram synthesis for irregular multi-layered media problem, I shall present the theoretical development for the 2D P-SV case. Following the similar procedures developed for solving the SH problem presented in an earlier article (Chen, 1990), I first set up the basic matrix equations starting from the basic boundary integral equations, then introduce and determine the global generalized reflection/transmission (R/T) matrices, and finally solve the basic matrix equations by using the global generalized R/T matrices. It can be demonstrated that for the case of horizontally layered media (a special case of the general model), the general solution derived in this study naturally becomes identical to that of the generalized reflectivity method, which is directly developed for horizontally layered media. Therefore, this new method can be viewed as an extension of the generalized reflectivity method to the case of irregular multi-layered media. For the problems of seismic ground motion and irregular topography, I derive the simplified formulas. This new method can provide an efficient, accurate, and unified algorithm to calculate the synthetic seismograms for a variety of the laterally heterogeneous media.