Carbon nanotube (CNT) is considered as a new generation of material possessing superior mechanical, thermal and electrical properties. The applications of CNT, especially in composite materials, i.e. carbonnanotube reinforced polymer have received great attention and interest in recent years. To characterize the influence of CNT on the stress intensity factor of nanocomposites, three fracture modes (opening, shearing and tearing) are considered. The stress intensity factor of nanocomposites is evaluated using a representative volume element (RVE) based on the continuum mechanics and finite element method (FEM). Inter-atomic interactions of CNT are simulated by beam elements in the finite element (FE) model. Non-linear spring based line elements are employed to simulate the van der Waals (vdW) bonds. In all fracture modes, the stress intensity factor was determined for pure matrix and matrix reinforced with single-walled carbon nanotube (SWCNT). Numerical results indicate that the load carrying capacities of the CNTs in a matrix are evident. Addition of CNTs in a matrix can increase the stiffness of the composite. Finally, the results showed that utilizing of SWCNT decreased the stress intensity factor and improved crack resistance.