Cycloid gear which was driven by three crankshafts and had three thin rims, was chosen as the subject of study. The bending stress of the rim and the tooth load of the cycloid gear were analyzed using the two-dimensional finite-element method when the gear had no machining and assembly errors and no backlash. Then the effect of the rim thickness on the bending stress and the tooth load were discussed, and the following conclusions were obtained. Both the bending stress of the rim and the tooth load are proportional to the applied torque. When the rim thickness decreases, the tooth loads decrease on the teeth located on the thin rim and increase on the teeth not on the thin rim. The ratio of the maximum tooth contact stress to the contact strength of the gear material is much larger than the ratio of the maximum bending stress amplitude on the rim to the bending strength of the gear material. Therefore, the tooth contact stress on teeth not located on the thin rim, not the bending stress, should be considered when designing cycloid gear with thin rims.