A strong-form based meshless random differential quadrature (RDQ) method is extended in a novel manner to fracture problems for computing the stress intensity factors (SIF), and called as extended-RDQ method (ExRDQM). The applicability of ExRDQM is successfully demonstrated in SIF computation of the single edge notched, double edge notched, and central cracked specimens under the mode-I and mode-II loading conditions. The ExRDQM consist of fixed-reproducing kernel particle method (fixed-RKPM) coupled with the local differential quadrature (LDQ) method and a novel strain computation approach (required due to uniformly or randomly distributed field nodes) combined with the correct boundary conditions specifically required by strong-form based numerical methods. The ExRDQM does not require: (1) nodal connectivity information for the shape function computation, (2) re-meshing (h-refinement), or (3) basis function enrichment, making it one of the alternatives to weak-form based methods (e.g. element free Galerkin method) and extended finite element method. The SIF in ExRDQM is numerically computed by: (1) displacement field interpolation method around the crack tip, and (2) modified crack closure integral method, and the results are compared with both the finite element solutions (ABAQUS) and analytical near-field expressions. The presented results show that the proposed methodology is efficient, accurate, and reasonably reliable while modelling the fracture problems, and it can very well be extended for the crack propagation in a near future. © 2022 Elsevier Ltd