When multiple cracks approach one another, the stress intensity factor changes due to the interaction of the stress field. This causes variation in the crack growth rate and shape of cracks. In particular, when cracks are parallel to the loading direction, their shape becomes non-planar due to the mixed mode stress intensity factor. In this study, the growth of interacting surface cracks was simulated by using the S-version finite element method, in which a local detailed finite element mesh (local model) is superposed on a coarse finite element model (global model) representing the global structure. First, simulations were performed for fatigue crack growth experiments and the method validity was shown. Second, simulations were conducted for various relative sizes and spacings of twin cracks. It was shown that the offset distance and the relative size were both important parameters to determine the interaction between two surface cracks; the smaller crack stopped growing when the difference in size was large. It was possible to judge whether the effect of interaction should be considered based on the correlation between the relative spacing and relative size.