Abstract: In this study, researchers discuss the frequency modes (first two modes) of non-homogeneous isotropic square plate on C-C-S-S condition where C and S represent clamed and simply supported, respectively. Here, thickness varies linearly in one direction. For non homogneity in the material, we considered circular varation in density. Bi-parabolic temperature variation on the plate is also being viewed. To find the vibrational frequency, Rayleigh Ritz technique has been applied for the different values of plate’s parameters.