The applicability of a wedge-joint mechanism with a curving wedge in presses for the implementation of metal forming separation processes was substantiated. The paper states the fact, that the wedge-joint mechanism graph of the deformation force change is the closest to the technological typical graph of the force change during separation. At the same time, the wedge-joint mechanism with a curving wedge has a lower height of the parts in comparison with the traditional crank mechanisms, which provides less elastic deformation and press dynamics. The use of the additional wedge mechanism in a press with the wedge-joint mechanism with a curving wedge to ensure the approximation motion is proved. This makes it possible to reduce the energy consumption for elastic deformation and further reduce the dynamic force. The mathematical models of the wedge-joint mechanism with a curving wedge, presented in the form of a two-slide link mechanism, were developed, allowing to perform its structural, kinematic and dynamic analysis. Based on the analysis of the proposed mathematical models, dependencies were identified and a procedure for calculating the geometric, kinematic and power parameters of wedge-joint mechanisms with a curving wedge for separation processes was developed. Comparison of the kinematic and dynamic analyzes results carried out by analytical and graphic-analytical methods confirms the reliability of estimates, since their discrepancy is not more than 2.5%. Experimental studies have confirmed the adequacy of mathematical models. The error between the calculated and measured values of the forces on the slide does not exceed 10%.