This study investigates the contact stress of concave conical involute gear pairs with non-parallel axes by means of finite element analysis. The complete mathematical models of the gear pair, including the working tooth surfaces and the fillets have been derived based on the theory of gearing and the generation mechanism. A mesh-generation program is also developed, which gives a dense mesh in the contact regions and a coarse mesh in the rest of the teeth. The commercial software, ABAQUS, capable of contact analysis of two 3-D deformable bodies is applied to evaluate the stress distribution on the tooth surfaces. Several numerical examples are presented to demonstrate the stress analysis of the gear pairs with various gear design parameters. The results show that the contact stress of non-parallel-axes concave conical involute gear pair can be reduced significantly by choosing grinding wheel with smaller radius. Therefore, concave involute gear pairs relieve the high contact stress problem of non-parallel-axes conventional conical involute gear pairs.