Abstract: By using linear vibration theory of thin elastic plates, the free vibration and thermal-buckling of the inplane constrained isotropic annular plates with axisymmetrical variable thickness and subjected to a inplane temperature rising are studied. Using finite difference method and considering the plates with exponentially and linearly variable thickness separately, the linear frequencies and critical temperatures of the plates with simply supported and clamped boundary conditions are calculated. The numerical results show that a linear relation between the square of the natural frequency and temperature exists. The parameters that characterize the variation of thickness and the ratio of the inner and outer radius of the plate have apparent effects on the natural frequency and critical temperature.Many numerical results are given in this paper which provide a reference for engineering design.