Abstract: The cycloid ball engagement pair has a configuration of spatial surface engagement, and the mechanical properties of engagement pair are affected by the nonlinear relationship between load and deformation as well as the extension of contact zone. Firstly, this paper establishes the nonlinear mechanical model of engagement pair using the hyperstatic method, and the time-variant engagement force is derived according to the equal work between engagement force and resistance moment. Then, the engagement force is converted to an ellipsoidal distributed load acting on contact zone. The deformed deflection surface of contact zone, the stresses under contact surface, and the depth of maximum shear stress are obtained using the superposition method, which integrates the deformation and stress of infinitesimal contact zone acted by concentrated forces. Finally, based on the position equation of balls, the finite element models of engagement pair are established with different engagement positions. The engagement process is simulated by the finite element method, and the stress distribution of engagement pair as well as the equivalent stress on engagement point is analyzed. The results show that the nonlinear mechanical model and the distributed load reduce the error caused by the simplification of linear elasticity and concentrated forces, and offer a more practical loading condition of engagement pair.