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A mathematical model is presented here to study the free vibrations of homogeneous rectangular plate of variable thickness which is clamped at all four edges. The main objective of the present study is to help the engineers and practitioners in designing various structures in the field of science and technology. The analysis is presented here to study two directional thermal effects with bi-linearly varying thickness. Rayleigh-Ritz method is used to calculate time period for first two modes of vibration for different values of thermal gradient, taper constants and aspect ratio. All the results are presented in form of tables for an alloy of Aluminium, ‘Duralumin’.