Flexural wave motion in a heat conducting thermo elastic doubly connected polygonal plate is studied by using the Fourier expansion collocation method. The equations of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of generalized thermo elastic plate of polygonal cross-sections composed of homogeneous isotropic material. The frequency equations are obtained by satisfying the boundary conditions along the inner and outer surface of the polygonal plate. The numerical calculations are carried out for triangular, square, pentagonal and hexagonal cross sectional plates. The computed non-dimensional frequencies are compared with the Lord-Shulman (LS), Green-Lindsay (GL), coupled Theory (CT) theories of thermo-elasticity and they are presented in Tables. The dispersion curves are drawn for non-dimensional frequencies of thermally insulated and isothermal boundaries.