Finite element modelling provides a great deal of support in the understanding of technological processes. However, there are few studies of the slitting process, and those that exist are simplified for use only in the calculation of steady states of such processes. This paper proposes the application of variational and finite element methods for the analysis of slitting and the nonlinearities of this process. Physical and mathematical models of the process and a new thermo-elastic/thermo-visco-plastic material model are elaborated. The procedure is implemented in the finite element code ANSYS/LS-DYNA and the model is validated comparing the numerical and experimental results. The influence of various process conditions on the strain and stress states and the quality of the final product are analysed. The results lay the groundwork for further study regarding the numerical analysis of spring-back behaviour and the effect of tool elasticity on the quality of the final workpiece.