In the article, based on the solution of the volumetric edge-contact problem, a method for calculating the load distributed over the contact area in meshing spur and barrel-shaped teeth for the case of their contact in the presence of a skew angle, has been developed. The method takes into account the following issues: the actual clearance factor in the neighborhood of the teeth flanks point of contact and the location of this point on the flank of a spur or barrel-shaped tooth at a known skew angle; the final dimensions and bending-shearing deformations of the teeth; edge effects when the contact area runs over one or both ends of the tooth. Based on an example of a study of an electric locomotive traction cylindrical gear, the results of calculating the distribution of specific load and contact stresses over the contact area for a spur-tooth and barrel-tooth gearing with different contact localization values under the skew angle variations have been put forward. The method makes it possible to implement a procedure for synthesizing the geometry of barrel-shaped teeth gears under specified operating conditions.