In this paper, the displacement discontinuity fundamental solution (DDFS) c
orresponding to the unit concentrated displacement discontinuity for three
dimensional (3D) non-local elasticity under symmetrical condition is obtain
ed. Based on the displacement discontinuity boundary integralequation (DDBI
E) and boundary-element method (DDBEM) of local (classical) elasticity, a m
ethod of analysis of crack in 3D non- local elasticity with wide applicatio
n is proposed with the DDFS. Through the method, several important problems
of fracture mechanics are analysed.