In this paper we consider the Non-homogeneous oscillatory flow of a vertically stratified fluid between two vertical porous plates, induced by suction and injection at the porous walls. Within the frame work of Boussinesq approximation for density, complete solution is obtained using similarity transformation and interpreted. The axial cosplay demon slayer and transverse velocity profiles and the pressure distributions are evaluated and illustrated in the figures. The results presented here add one more class of exact solution S.Ganesh [8] Rajagopal [14], Wang [22] to that of a few presently available in literature. The result for the axial velocity obtained here reduces to the result for the axial velocity in the case of laminar flow between parallel plates (i.e., when v = 0).