The structure and transmission principle of the end face engagement cycloid steel ball planetary transmission are introduced in this paper. The complicated spatial mechanics model for multi-steel ball （multi-point contact of each ball） engagement pairs of the cycloid groove is established. The maximum acting force formula of the cycloid groove engagement pair is deduced by using ultra static distortion harmony conditions. The contact stresses of the cycloid groove are analyzed by Hertz stress theory

and the stress variety curves are drawn. The research results are important for the theory research and application design of this transmission.