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Cohesive zone model is widely used in fracture mechanics,and when the fracture process zone(FPZ)in front of the crack tip is too large to be neglected,the nonlinear behavior must be considered.That is to say in this circumstance the linear fracture mechanics is no longer suited.In order to take into account the nonlinear behavior in FPZ,many fracture models were proposed.And among all of these models,perhaps the cohesive zone model(CZM)is the one which is simplest and has been widely used.In CZM,the FPZ in front of the crack tip is assumed to be a very narrow strip(cohesive crack)in which the upper and the lower surfaces are held by cohesive tractions and the stress singularities vanish in the cohesive crack tip.Cohesive tractions are depended on the cohesive surface separation,and the relationship between cohesive traction and the separation is termed as cohesive law or traction-separation law,which is determined by material physical properties and also considering mathematical simplicity.And the cohesive crack starts to propagate when the stress at the crack tip reaches the cohesive strength and the energy supplied by the structure is enough to create a new cracked area.In the previous studies,many numerical methods such as finite element method(FEM),boundary element method(BEM)and so on were proposed.The most widely used method is FEM,but there still remain some problems when CZM was incorporated into FEM,such as inaccurate FPZ length,extremely refined mesh,difficulty to convergence and so on.In order to get over these difficulties,a new analytical singular element is proposed in the present study.In this singular element,the cohesive traction is approximately expressed in the form of polynomial expanding though Lagrange interpolation.Special solution corresponding to each expanding term is specified analytically.Each special solution has strictly satisfied the requirements of both differential equations of interior domain and the corresponding traction expanding terms.So the real cohesive traction acting on cohesive crack surface is expressed in a nature and strict way,which of course will bring in significant contribution on the prediction of the nonlinear response.Then the special solution can be transformed into nodal forces of the present singular element.Assemble the stiffness matrix and nodal force into global FEM system,cohesive crack propagation can be modeled.An efficient iteration method in implicit manner is also proposed to solve the nonlinear problem.Finally,the cohesive crack propagation under arbitrary external loading can be simulated,and the length of FPZ,crack tip opening displacement(CTOD)and other parameters in the crack propagation can be obtained simultaneously.The validity of the present method is illustrated by numerical example.