Modes I and II stress intensity factors are analyzed by means of a variational boundary integral method (VBIM) for slant surface-breaking cracks in a half-plane with surface steps subject to contact loadings. This method represents the crack as a continuous distribution of dislocation loops. The crack opening displacements, which are related to the geometry of loops and their Burgers vectors, can be determined by minimizing the elastic potential energy, obtained from the known expressions of the interaction energy of a pair of dislocation loops, of the solid. In contrast to other methods, this approach finally reduces to a symmetric system of equations with milder singularities of the type 1/R, which facilitate the numerical treatments. By modeling the surface boundary of the half-plane as half part of an infinite crack breaking through an infinite solid, this paper demonstrates that the VBIM can be well extended to solve the fracture problems of inclined surface-breaking cracks in a half-plane with curve or step notches subject to combined contact loadings, and presents results of stress intensity factors for a variety of loadings, cracks and step surface configurations. Numerical results of test examples are in good agreement with the existing results in the literature.