Among the various processes involved in producing oil and gas, the drilling process has received great attention recently. Research is being directed to this issue in order to improve the performance of drill bits. Thus, the interest of the oil industry is to increase the penetration rate, reduce the time of switching, extending the life of drills and consequently reduce spending during the drilling process. To achieve these goals are traditionally used for drilling optimization methods based on mechanical specific energy. These methods use as input the weight on the drill penetration rate, torque and compressive strength of rock. The drilling optimization methods still present some difficulties, such as mechanical specific energy relationship with compressive strength and the methods depend on data-drilling, as listed above. This dissertation aims to present a study of alternative rock cutting process based on numerical simulation, specifically using a commercial finite element program called Abaqus. The first part of the work was the development of models of metal cutting based on the plasticity law of Johnson-Cook. The motivation in choosing these models was the large number of studies in the literature dealing with the machining process in metals. Subsequently, the second part of the work, which is cut in rock, was conducted. Three-dimensional models of single cutter tests were designed and simulated using the plasticity law of Drucker-Prager, suitable for rocks, which considers the effect of confining pressure.