In this paper, primary manufacturing and assembling errors of three-ring gear reducer (TRGR) are analyzed. TRGR is a new transmission type whose eccentric phase difference between middle ring plate and side ring plates is 120°. Its mass of middle ring plate is equal to that of side ring plate or 180°, and its mass of middle ring plate is twice of that of side ring plate, which affects load distribution between ring plates. The primary manufacturing and assembling errors include eccentric error of eccentric sheath Em, internal gear plate Er and output external gear Eic. A new theoretical method is presented in this paper, which converts load on ring plates into the dedendum bending stress of ring plate to calculate load distribution coefficient ( LDC ), by means of gap elenent method (GEM), one of finite element method (FEM). The theoretical calculation and experimental study, which measures ring plate dedendum bending stress by means of sticking strain gauges on the dedendum of middle ring plate internal gear and side ring plate internal gears, are presented. The theoretical calculation and comparison with experiment result of LDC are implemented on two kinds of three-ring gear reducers whose eccentric phase difference between eccentric sheaths is 120° and 180° respectively. The research indicates that the result of theoretical calculation is consistent with that of experimental study. That is to say, the theoretical calculation method is feasible.