The forces acting in the process of single point incremental forming (SPIF) change the geometry of the sheet metal. The tool-workpiece interaction process is non-linear due to the large deformations of the sheet metal, which determine the plastic behaviour, as well as the evolutionary boundary conditions resulting from the contact between the tool and the sheet. Instead of lubricating the contact surface of the forming tool and the sheet metal, an innovative environmentally friendly method to reduce the coefficient of friction by vibrating the sheet has been proposed. The finite element method (FEM) allowed a virtual evaluation of the deformation parameters of the SPIF process in order to determine the destructive loads. The FEM was chosen as a deterministic numerical tool to evaluate the set of defect parameters induced by forming forces. The paper also proposes a method for predicting the formation force using an artificial neural network (ANN), assuming that such a model is generalized to implicit data. In this context, an empirical analysis of the implementation of the ANN technique is performed.