Simulation of fracture by using numerical methods is important to treat geometries that change in time. In this study, both numerical and experimental investigations are presented for the delamination under mode II loading, detailing the derivation of the formulations in numerical simulations of fracture. The simulation of the delamination under mode II loading based on the cohesive segments model was investigated by using a mesh-free method. Then, an experimental investigation was used to verify the meshfree method's results. For tests under mode II loading, three-point end-notched flexure specimens, which are made of carbon/epoxy laminate (AS4/3501-6) which consists of 10 plies in (10) and [0/90/0/90/0](s) lay-up with delamination inserted in the middle of the laminate, were used for the interlaminar fracture toughness tests. The problem was solved for  10, [0/45/-45/90/0](s), [0/90/0/90/0](s), [0/90/0/90/30](s), [0/90/0/90/45](s) and [0/90/0/90/60](s) laminates with midplane delaminations, and the results were verified for different composite materials. The critical fracture force, which can be experimentally measured, was used to calculate the mode II delamination fracture toughness of the carbon/epoxy laminate. In addition, values of the integral for 209 (11x19) and 253 (11x23) background meshes with equivalent interval sizes were compared. For a relatively fine background mesh, the critical load was converged. Results obtained from the meshfree element-free Galerkin method showed very good agreement with experimental data for single-mode delamination under mode II loading. The results presented will help in the implementation of mesh design techniques that protect numerical accuracy while minimizing computational expense.