A non-isothermal rarefied gas flow trough a long tube with an elliptical cross section due to pressure and temperature gradients is studied on the basis of the S-model kinetic equation in the whole range of the Knudsen number covering both free molecular regime and hydrodynamic one. A wide range of the pipe section aspect ratio is considered. The mass flow rate is calculated as a function of the pressures and temperatures on the tube ends. The thermomolecular pressure effect has been modeled and the coefficient of the thermomolecular pressure difference has been calculated in whole range of the Knudsen number and in wide range of the pipe section aspect ratio.