This paper presents a new enhanced computational model of Ultrasonically Assisted Turning (UAT) that is based on the DEFORM 3D FE code and allows transient, coupled thermo-mechanical simulations of both UAT and Conventional Turning (CT) of elasto-plastic materials. The model features 3D oblique chip formation and realistic geometry of a cutting tool. The model is used to analyse the effect of cutting and vibration parameters on cutting forces in UAT. The comparison between efficiency of various vibration directions is also carried out. Optimum values for cutting and vibration parameters are suggested as a result of this numerical study.