A computational method to simulate rock cutting is developed and evaluated within this work. It aims to obtain the forces on the pick during cutting. The explicit FEM is chosen to model the pick-rock interaction. It allows accelerated calculations due to parallelization, a robust contact algorithm and superior material description with constitutive equations. The mechanical behavior of rocks is analyzed and broken down into single attributes that outline the requirements for the constitutive equations. A damage-plasticity law is chosen and modified with user-subroutines. The expected critical mesh distortions are evaded by introducing an element deletion routine. The boundary is modeled with infinite elements to suppress acoustic wave reflection and unrealistic interference. A probabilistic material model is developed based on the Weibull theory to assess the brittle and flaw-dominated fracturing of rocks. Earlier approaches taken from the literature turn out to be inadequate. The present material model covers the natural scatter of experiments but the material does not exhibit a more realistic crack growth. Therefore the classical homogeneous material modeling is used for further calculations. The constitutive equations are calibrated by fitting the yield function numerically to stress states that cause fracture. These stress states are obtained from inexpensive Brazilian tests and uniaxial compression tests. An eccentric tensile stress peak in the Brazilian test specimen is found close to the loading plates. High-speed camera images emphasize that the origin of fracture is most likely not in the center of the specimen as assumed previously but close to this stress peak. Comparison of tensile test results with Brazilian test results reveal the problem of a one-parameter tensile strength. The tensile strength is extended to a two-parameter description of tensile strength and loaded volume using the Weibull theory. This method allows to calculate the tensile test, the Brazilian test and the edge chip-off test correctly. The individual concepts are combined to set up a cutting model for parametric studies. First, ideal picks (conical and a semispherical) are tested with the model. Crushing, chipping and undercutting are observable depending on pick geometry and cutting parameters. However, element deletion proves to be problematic for the contact between pick and rock. Second, a worn pick is modeled and cutting depth and attack angle are varied. The calculations show that the cutting force increases with cutting depth as expected. No effects of the cutting parameters on the normal force are found. The reason is that the crushed zone beneath the pick cannot be covered in the FE simulation. Nevertheless, material crushing clearly correlates with force peaks in the simulation. A direct comparison of the simulation with the corresponding experiment reveals that the cutting force can be predicted but the simulation underestimates the normal force and the side force. The reason for this underestimation is the erosion of the crushed zone in the simulation. Analyzing the chipping event shows that the simulation leads to smaller chip sizes than the experiment. The developed concepts in this work allow an adequate rock material modeling and the simulation of basic mechanisms in rock cutting.