By means of differential geometry principle, derives the main curvature and main direction of the tooth surface of face-gear drive, and obtains two principal values of the induced normal curvature in the face-gear drive. Analyses the impacts of main parameters on the curvature in the face-gear drive, and according to the relations of main curvature on contact point and elastic coefficient of two elastomers to the contact ellipse area, determines the face-gear meshing contact area; at the same time, analyses the tooth surface contact pressure distribution and variation of face-gear driving in the ideal meshing condition and also makes a simulation analysis. The results show that: in the face-gear meshing process, the tooth surface contact stress along the tooth width direction becomes larger close to the edge at both ends and maximum near the outer edge, while minimum in the center of the tooth surface. Therefore, the face-gear drive should consider the tooth surface modification, make the contact point of face-gear meshing near the middle of the tooth surface, in order to improve the carrying capacity of the face-gear and reduce the impact when the tooth meshing in and out.