Patterns of dike swarms around volcanic centers or above mantle plumes are interpreted by a mechanical analysis of regional and dike-induced stresses, in which dike emplacement is controlled and guided by the stress state. Comparisons of dike patterns with patterns of principal-stress trajectories caused by a source and a regional stress system are commonly used to infer paleostresses. However, dike trajectories are determined by a complex interaction between dike-induced stresses and the source/regional stress system. We present numerical calculations based on a novel boundary-integral formulation, which examines the simultaneous effects of regional stresses, magma pressure, and dike injection on the local stress state around a continuously curving dike. Dike paths are calculated from the condition that dikes propagate by mode I failure. Our results suggest that the magnitude of the regional stresses would be 2--5 times higher than previous estimates based on principal-stress trajectory analysis.