A three-dimensional subsurface penny-shaped crack in an elastic half-space subjected to a compressive moving load is analyzed using the finite element method. The compressive load is applied through a spherical asperity, which moves from left to right on the top surface of the half-space. Normal contact between the crack faces of the penny-shaped crack is modeled using the classical Lagrange multiplier method for constraint enforcement; the tangential contact between the crack faces is assumed to exhibit frictional behavior. Therefore, although the present analysis is limited to a purely linear elastic quasistatic approach, the analysis results show the loading path dependence caused by the frictional contact. Based on linear elastic fracture mechanics, stress intensity factors along the crack front of the penny-shaped crack are evaluated as functions of the crack-front angle, frictional coefficient, normalized load position, and the ratio of the crack depth to the crack length. Finite element analysis shows that shearing-mode failure rather than tearing-mode failure is the dominant cracking mechanism of the penny-shaped crack. This shearing-mode failure tends to occur in the direction of the loading path.