In the modern technology, the plates of variable thickness are widely used in engineering applications i.e. nuclear reactor, aeronautical field, naval structure, submarine, earth-quake resistors etc. In this paper thermal gradient effect on vibration of square plate having one -direction thickness variations is studied. The non-homogeneity is assumed to arise due to the variation in the density of the plate material. Rayleigh Ritz method is used to evaluate the fundamental frequencies. Both the modes of the frequency are calculated by the latest computational technique, MATLAB, for the various values of taper parameters and temperature gradient. All the results are presented in the graphs