In this paper, the exact forms of integrals in the meshless local boundary integral equation method are presented and applications were demonstrated for fracture mechanics. A weak form for a set of governing equations with a unit test function or polynomial test functions is transformed into local integral equations. Each node has its own support domain and is surrounded by a local integral domain with different shapes of boundaries. The meshless approximation based on the Radial Basis Function (RBF) is employed for the implementation of displacements. For cracked plate, opening displacement on the crack surface can be obtained with satisfactory accuracy without special treatment for stresses singularities at crack tip.