The study of the stress state and power parameters when pulling workpieces in a special die with an inclined working surface at various shapes of the plastic deformation zone and geometric parameters of the special die was conducted. The distinctive feature of the proposed special die and the metal treatment process in the working channel of this die was described. The theoretical provisions and assumptions from the fundamental theory of plasticity and metal forming were used. The influence of the intensity of shear deformations on the stress state and force at the angles of inclination of the working surface of the die within 45–20°, the value of the ratio of the diameter of the workpiece to the length of the inclined surface d/z=1.5–2.0 was investigated. The optimal d/z ratio was determined by the method to a rigid punch indenting a rigid-plastic half-space, as well as by the method of strain energy. The field of slip lines and hodographs of velocities for various shapes of the deformation zone and geometric parameters of a special die were constructed. Based on the constructed slip line fields and velocity hodographs, the mean stress and stress components at the nodal points of the slip line field with the compilation of the equilibrium equations for all forces applied to the plastic zone were calculated. The study of the influence of contact friction between the working surface of the die channel and the workpiece on the stress state and power parameters during pulling was carried out. It was revealed that the optimal ratio d/z=1.5 and the optimal angle of inclination of the working channel of the die α=20°. It was found that for these parameters in the zone of plastic deformation, mainly significant compressive stresses act, which favorably affect the obtaining of a homogeneous and refined microstructure, and also exclude the appearance of anisotropy due to the implementation of maximum shear deformations in the workpiece.