An internal gear with thin rim which meshes with three planet gears in a planetary gears is chosen as the subject to the study. The stresses in the internal gear with various rim thicknesses and numbers of teeth are analyzed by the finite element method, and the bending strength is considered. As the result of the study, the following are obtained. In the case of the thin rim, it is necessary to consider the stresses on the fillet of neighboring tooth in the direction of load to the loaded tooth and on the fillet at an angle of almost 30° in opposite direction of load from the loaded tooth as well as the stresses on the loaded tooth fillets. The thiner the rim, the lower the bending strength becomes as the fillet stresses become large and reversed stresses. Furthermore the larger the number of teeth, the lower the bending strength becomes in the case of the thick rim, but the smaller the number of teeth, the lower the bending strength becomes in the case of the thick rim.