In this paper, the damping of generalized thermo elastic waves in a homogeneous isotropic plate is studied based on generalized two dimensional theory of thermo elasticity. Two displacement potential functions are introduced to uncouple the equations of motion. The frequency equations are obtained by the traction free boundary conditions using the Bessel function solutions. The numerical calculations are carried out for the material Zinc and the computed non-dimensional thermo elastic damping factor is plotted as the dispersion curves for the plate with thermally insulated and isothermal boundaries.