Abstract: By means of the boundary conditions of the crack, a system of singular integral equations is obtained. Using the numerical method for the solution of the singular integral equations, the stress intensity factors at the tip of a branched crack in the gear surface loaded by Hertzian contact stresses can be calculated. From the current theories about a crack propagation, the tip of the branched crack spreads to the surface in the direction of about to 60° with the declined crack.