Abstract: In order to analyze the crack growth by thecohesive zone approach in a general structure, the concept of generalizedcohesive interface is proposed. Based on the principle of the energyrelease rate and the linear elastic equivalence of the cohesiveinterface, the element'sstiffness matrix is obtained. On this basis, the load/displacement functionof the double cantilever beam(DCB) is obtained, under pure mode Icondition. With the software BAQUS, the numerical simulation ofdelamination'sgrowth is carried out. Analytic functions and numerical simulation's resultsshow that the generalized linear elastic cohesive zone equivalence isvalid.