The influence of carbon nanotubes (CNTs) on the fracture behaviour of composites is studied. A 3-D finite element model consisting of CNT, interphase and surrounding polymer is constructed. CNT is modeled as a lattice structure using beam elements and the interphase region is simulated using non-bonded interactions. A semi-circular crack is considered in matrix and boundary conditions are adapted reflecting fracture mode I. The J-integral is obtained for both neat resin and CNT reinforced polymer. The results demonstrate importance of considering CNT as a lattice structure and taking into account interphase region.