Heat-resistant alloys like Inconel 718 are used in critical components such as aircraft engine turbine discs. Surface integrity is a critical issue in this kind of components and specially residual stresses are a key aspect. Currently, the development and optimization of the machining process with regards to the residual stresses is done through expensive experimental trial and error methods. This article shows the research work made on the development of a machining model in three dimensions with the finite element code Abaqus / ExplicitTM aiming to predict residual stresses. Results obtained in different working conditions are compared with those of commercial programs as DeformTM and AdvantEdgeTM, so as with experimental results obtained in turning. The results obtained show on the influence of working conditions (cutting speed, feed per revolution) on the cutting forces and temperatures and the high degree of qualitative agreement with finite element modeling in the generation of surface residual stress.