Equal channel angular pressing is one of the most prominent procedures for achieving ultra-fine grain structures among the various severe plastic deformation techniques. In this study, the effect of superimposing ultrasonic vibration on the punch during the equal channel angular pressing process was investigated by finite element model. Two different 2D plane strain models were considered in the simulations. In the first model, the die and the punch were considered as rigid bodies and in the second model, the punch was considered as an elastic body. Both models showed reduction in the forming force. These models also showed that this force reduction depends on the vibration amplitude and the die velocity. However, the amount of reduction was lower in the second model because the amplitude of 10 µm at the working surface of the punch reduced to 1.25 µm in forming situation while in the first model remained constant i.e. 10 µm. It was shown that this amplitude reduction during forming is more realistic in comparison with constant vibration amplitude. The reduction of amplitude depends on the work material and punch material and in this study they are AL1100 and Ti-6Al-4 V, respectively. By using a 3D finite element model and an elastic punch also showed that the second model is more realistic if compared with experimental data.