In this paper computer simulation of cutting process dynamics in turning, using a mechanistic cutting force model, is significantly enhanced by incorporating a dynamic ploughing force model. The ploughing forces are decomposed into static and dynamic components. The effect of tool feed on increasing the clearance face contact is described mechanistically. The ploughing model is developed for the complex geometry of a multi-edge cutting tool and the effect of integrated tool/workpiece vibrations is considered. The cutting process damping is predicted by tracking the dynamic ploughed volume resulting from the interaction with machined surface undulations. The model has been used through computer simulations to predict the cutting forces and machined surface errors. The results clearly demonstrate the effect of including the ploughing model on the process dynamics. The theoretical predictions show a good agreement with the experimental results.