In this research, initiation and propagation of delamination are investigated using finite element analysis and existing theories for isotropic and composite double cantilever beam (DCB) specimens. These theories work based on the well-known traction-separation laws such as linear, bilinear and exponential laws. In addition, the effects of cohesive zone parameters, i.e., critical strain energy release rate and maximum interfacial stress, transverse shear deformations and fiber bridging law are studied. The results show that the introduced theories and finite element analysis based on bilinear cohesive law are not capable to predict initiation and propagation of delamination in unidirectional composite specimen with fiber bridging effect and neglecting this region in CZM cause significant error in prediction of delamination growth. For this purpose, bilinear CZM considering bridging law is modified and implemented in 3D finite element analysis. Comparing numerical results with available experimental data in the literature shows that finite element models based on modified CZM can predict initiation of delamination as well as propagation accurately.