This paper reports on the free vibration solution of a thick plate by using three dimensional coupled thermoelastic theory. Many previously works reveal that the mechanical and thermal are coupled together, which mean that the deformation of the solid will produce temperature variation inside the solid. First, based on the three dimensional coupled thermoelastic theory, the governing equations of the thick rectangular plate for free vibration analysis are derived. Unlike the traditional first order or third order shear deformation theory with which the deformations along the thick direction are described by the deformations of the middle surface, a new form which use functions to describe the deformations along plate thick direction (the z direction) is presented in this paper. Galerkin method and Laplace transform are applied to convert the governing equations into a series of first order ordinary differential equations as well as the boundary conditions to obtain the closed solution of the coupled thermoelastic rectangular plate. The Newton iterative method is applied to solve the eigenfunction. Finally, a thick plate with four edges simply supported has been investigated by using the proposed method. Eigensolutions and the damping effects of the plate with thermoelastic coupling are investigated by numerical example
