A method to apply the approximation formulae[1] for tooth fillet and root stresses of a thin-rimmed rack to the calculation of stress state of thin-rimmed external and internal spur gears is introduced. The stress values by the method proposed in this paper have shown good agreement with those by the REM analysis and also by the stress measurement of strain survey investigation. By this method, reliable stress state at tooth fillet and root areas in the thin-rimmed external and internal spur gears can be easily calculated, and a practical design method for the bending strength of such thin-rimmed gears is established.