This paper deals with modelling of the orthogonal machining process using tools with different geometries. The finite element method (FEM) is used for a simulation based on the Lagrangian formulation including ANSYS/LS-DYNA software. The constitutive Johnson – Cook material model regarding strain, strain rate and temperature to predict material plasticity and chip separation is used. Chip morphology, stress, strain, strain rate, residual stress and temperature have been obtained for a range of tool rake angles, cutting edge radii and friction coefficient values. Results are compared with experimental results and other references.