The mechanical model of meshing pair was built. Force of two meshing pairs and turning arm bearing were analysed. The contact stress of hypocycloid and epicycloid tooth surface was deduced with Hertz theory. Their stress change curves were drawn with different tooth number. The results show that the contact stress decreases when the tooth number increases. And,the maximal contact stress presents to the inner tooth surface of hypocycloid groove. Real example is built and the maximal contact stress is calculated by Matlab. This research provides important theory basis for the design application of the cycloid ball planetary transmission.