The understanding of rock cutting mechanism is critical to the efficiency of borehole drilling process. This mechanism is studied through single cutter tests. In this work were developed models with the Finite Element Method to simulate the rock cutting process by a single cutter. This work is connected to the project Modeling of Evaporite Drilling Under High Pressure, sponsored by Baker Hughes in partnership with the Group of Technology and Petroleum Engineering (GTEP) of the Pontifical Catholic University of Rio de Janeiro. The numerical simulations were performed using the program ABAQUS. The Drucker- Prager constitutive relationship was used to model the rock behavior. Also, an isotropic model of damage was described and employed for modeling the erosion mechanism that represents the rock-cutter interaction. Two and three-dimensional simulations allowed the analysis of the influence of the variation of cutting depth and confining pressure on the mechanical specific energy required to cut the rock. To certain depth limit, it was observed that for larger depths of cut, less specific energy is required to cut the rock. The analysis of experiments under confining pressure showed that cutting process under atmospheric conditions produced specific energy close to the unconfined compressive strength of rock, while the application of confining pressure showed a remarkable increase in specific energy required for cutting.