The paper describes a mathematical model of the electron beam positioning process along the junction during the electron-beam welding. The model comprises the decision of the following interrelated tasks: taking into account the influence of a focusing and deviating systems of the automatically controlled electron beam technological complex on the position of the electron beam, analytic definition of the total error of mechatronic modules, taking into account the dynamic characteristics of a mechatronic complex, and definition of the transient process time of the ith mechatronic module. The developed mathematical model will allow obtaining an ultimate pattern of the electron beam positioning process during the electron-beam welding when producing the spatial weld seam of an arbitrary shape with account of the majority of determinative factors in real time.