The development of analytical techniques describing rock fracture during drilling would make possible a more rational approach to the design of drills and bits. In this paper we describe progress toward this goal based on finite element and experimental investigations of the rock cutting process for a single drag bit. The material model used for rock in the analysis includes fracturing due to both tensile and shear stresses. Results capture the essential features of drilling observed in the laboratory and indicate expected differences between unconfined laboratory tests and downhole drilling.