<p>This paper uses two imaginary flat rack cutters with tooth profile modification to generate spherical gear pair with toroidal surface. The two tool profiles are straight-line profile and parabolic profile. The equations of the surface family of the flat rack cutters can be obtained from the homogeneous coordinate transformation matrix. According to the two-parameter meshing theory, the equations of meshing between the spherical gear and the flat rack cutter with unmodified tooth profile (straight) or the spherical pinion and the flat rack cutter with modified tooth profile (parabolic) were obtained. By substituting the equations of meshing into the equations of the surface family of the flat rack cutters, the geometric models of the spherical gear and spherical pinion can be created. The artificial assembly error was designed and the tooth contact analysis method was used to analyze the impact of the assembly error on the transmission error and the tooth surface contact. A computer program calculates the contact tooth marks of the spherical gear pair during rotation and observes the contact situation of the tooth pair. The spherical gear pair with this shape of teeth can bear the load smoothly.</p>