A theoretical development of formulae for the definition of a speed of welding deposition on a flat is presented where in the first case cross oscillations are applied on it and in the second one – longitudinal oscillations. The law of oscillation motion for both variants and also the law of sinusoidal oscillations of a welding tool are specified. In such a way, the computation of the rate of welding deposition in both cases is carried out under conditions of an additive oscillation effect. The realization of continuity conditions with the application of a heating source motion according to a sinusoidal law at a motionless surface to be under welding deposition – a uniform formation of a beaded weld on a width which is characterized by the position of a continuity point is assumed as a basis of the computation. In case of a shift of the surface under welding deposition this condition will change considerably as a point of continuity will be shifted in which connection in the first case – crosswise, and in the second – lengthwise. The module of the shift of this point is specified by a differential equation which describes motion character equally both at longitudinal and transversal shift of the surface under welding deposition. Final expressions for a welding deposition rate will differ that is caused by a difference in a mathematical description of a continuity condition.