Abstract: A mathematical model is presented to study the effect of circular variation in density (as a non-homogeneity parameter) and linear variation in thickness to natural vibration of square plate on clamped (C-C-C-C) boundary condition under temperature enviornment. It is considered that the temperature variation along both the axes are parabolic. To obtain frequency modes, Rayleigh Ritz technique has been applied. All the results are presented in the form of tables. Comparison of the result with existing result (in literature) is also presented in the form of figures.