In the present paper, the line-spring model originally proposed by Rice and Levy is combined with the boundary element method to analyze the stress intensity factors of cracks in three-dimensional structures. The line-spring boundary element method proposed here greatly reduces computer run time, since it enables one-dimensional analysis of three-dimensional crack problems. The present method is first applied to the stress intensity factor analysis of an embedded elliptical crack to study the effects of types of boundary element, i.e. the constant, linear and quadratic elements, and boundary element mesh on the accuracy of the solutions. Furthermore, it is also applied to the stress intensity factor analyses of interacting elliptical cracks, that is, closely located or partly overlapped twin cracks, to clarify the interaction effect of cracks. The calculated results are compared with those of ASME Boiler and Pressure Vessel Code, Section XI, Appendix A.