In the present work, frequency equations are obtained for Rayleigh-Lamb wave propagation in a transversely isotropic plate of thermoelastic material, in the context generalized theory of thermoelasticity. The thickness of the plate is taken to be finite and the faces of the plate are assumed isolated and free from stresses. The analytical solution for the temperature, displacement components and stresses are obtained by using the eigenvalue approach. The frequency equation corresponding to the symmetric and antisymmetric modes of wave propagation of the plate are obtained. The function iteration numerical scheme is used to solve the complex frequency equation, in order to obtain phase velocity and attenuation coefficients of propagating wave mode. The results have been verified numerically and are represented graphically.