Abstract: Making use of the Betti reciprocal work theorem, this paper derives the general fundamental solutions of displacement discontinuity in three dimensions, and then establishes the displacement discontinuity super-singular integral equations to solve three-dimensional multi-crack problems, in which the super-singular integral calculations are given by adopting the triangle element transformation and the finite-partial integral, and the angular point problems are solved by introducing inharmonical elements. Finally, stress intensity factors can be directly calculated by the discontinuity displacements of cracks.