The article proposes the implementation of a novel method of plastic forming of internal toothing in flange spline sleeves. A method being the subject of Polish patent application P.416772 has been used for this purpose, which involves a combination of the scheme of the direct extrusion of a cone hollow with the die press forming of the wall to obtain a flange. The entire process takes place in a single technological sequence. The operations come one after another, so that there is no need for reheating the stock or carrying out intermediate soft annealing. The proposed method is assumed to be an alternative to the operation of press forming of internal spline sleeve toothing in a conical die  and to the operation of swaging on rotary swaging machines . It is assumed that this method, too, is alternative to other technologies known from the literature and industrial practice, whose specifications and literature references will be indicated later on in this paper. Computer simulations of the flanged sleeve plastic forming process were performed using the commercial numerical program Forge®3D. During the numerical computations, the distributions of temperature fields were determined on the cross-section of the plastically formed product. The computations enabled also the visualization of the plastic flow of metal, especially in the toothing forming regions, and the determination of the energy and force parameters of the process.