Based on the meshing theory of gears, curvature interference characteristics of the straight bevel gear are studied in this paper. In this study, the tooth surface of straight bevel gear is cut by an imaginary flat top generating wheel, and the corresponding mathematical model is established. The tooth surface equation, meshing function and curvature interference limit function of the straight bevel gear are derived by utilizing vector operation and vector rotation transformation. The expression of the curvature interference limit line in the axial section is derived, and it proved to be a straight line passing through the origin of coordinate. In addition, it is found that undercutting is more likely to occur at the inner end of the straight bevel gear, which can be solved by reducing the tooth width appropriately. A numerical example is implemented, the obtained results reflect that there exists a curvature interference limit line. The tooth profile of the straight bevel gear and the curvature interference limit line in the axial section are drawn, the interference line isn’t located at the surface of the tooth surface, which means this straight bevel gear won’t occur undercutting. In addition, the minimum number of the straight bevel gear for no undercutting is calculated by using the back cone cylindrical gear theory, it is less than the actual number of teeth. These results are consistent, which verifies the correctness and feasibility of the theory proposed in this paper.