The paper presents the results of computer simulation of a new technology for forming and strengthening screw fittings, carried out using the planned experiment. The purpose of the simulation was to determine the parameters at which the deformation process is stable. The friction coefficient in the rolls, the distance of the matrix from the forming rolls and the initial diameter of the workpiece were selected as variable factors. The workpiece speed was considered as the main parameter and the model was considered unsuccessful if the front end of the workpiece had a zero value of speed (the workpiece was stuck). It was found that all three parameters have a significant impact on the process stability. The best parameters are an increase in the friction coefficient in the rolls and the initial diameter of the workpiece (or absolute compression in the rolls) and a decrease in the distance of the matrix from the forming rolls. Also, a rational factor that has a beneficial effect on the process is the reduction of backpressure from the matrix, which can be realized by reducing its length.