Use of vibration in the forming process has already shown numerous advantages in the improvement of mechanical and surface properties of workpiece such as good surface or less friction between die and workpiece. The aim of this work is to develop a mathematical model of a progressive wave in the lower die due to the vibration given by multi piezoelectric actuators to assist the forging process. Based on the mathematical model, simulations using nite element software Forge2011® have been performed to observe the presence of progressive wave in the workpiece due to the movement of the lower die. The simulations' results con rm the existence of progressive wave in the workpiece and demonstrate the e ect of progressive wave to reduce the forging load and improve the forging process.