Abstract： The inertial entropy theory was used to analyze the thermoelastic coupling free vibration problem of a simply supported homogeneous transversely isotropic thermoelastic cylindrical shell. By introducing the displacement potential functions, the equations for free vibration problems could be reduced to four secondorder ordinary differential equations and modified Bessel function solutions with complex arguments could be obtained that can describe the displacement, temperature and stress. Considering the tractionfree and thermally insulated conditions at the lower and upper surfaces of the shell, the free vibration equation could be obtained. The crystal of Zinc was chosen as the material. The numerical calculations show that the thickness of the shell has a greater impact on the lowest frequency with the increase of mean radiustolength ratio and the axial halffull wave number. The circumferential full wave number has a greater impact on the lowest frequency of thinnerwall shell. The lowest frequency decreases first and then increases with the ascent of the the circumferential full wave number. The increase of circumferential full wave number enlarges the influence of the thickness of the shell. The inertial entropy theory can get the exact solution with fewer parameters.