The purpose of this thesis is to develop numerical techniques to model and analyse metal forming operations involving material removal and ductile fracture. Due to the diversity and complexity of the physical phenomena involved, several different computational aspects of the problem have been addressed such as: computational strategies for general thermo-mechanical coupled problems accounting for heat generation due to plastic and frictional work, thermal contact, thermal strains and temperature dependent properties; ductile fracture criteria for damaged and conventional J₂ elasto-plastic materials; and transfer operators for thermo-mechanical coupled problems and error estimates for damaged and conventional J₂ elasto-plastic materials. The above techniques made possible studies on the following subjects: application of ductile fracture concepts to material separation in incipient chip formation and blanking; and application of error estimates and re-meshing procedures to high-speed machining. The technique developed in this thesis provide useful computational tools in the analysis of the phenomena involved in chip formation processes and constitute an advance with respect to numerical simulation of orthogonal machining.