Meshless Methods using kernel approximation like Reproducing Kernel Particle Method (RKPM) are methods for solving partial differential equations that require only nodal data and a description of the geometry without requiring element connectivity data and mesh producing. An innovative method of nonplanar material partitioning method (NMPM) with implementation of RKPM is employed to calculate the stress intensity factor (SIF) at the tip of an anticrack sited in an isotropic plate under a remote applied loading. Numerical examples in comparison with the exact closed form expressions show that accurate SIF for mode I can be obtained.