Abstract: In this paper,the express of the stress and displacement field of a dissimilar orthotropic laminate with an interfacialedg crack(delamination),under antiplane shear loading,satisfying all of the basic equations,boundary conditions along the crack surfaces and conditions of continuity along the ligament of the interface are obtained by the menthod of complex variable.Furthermore,the coefficient of the singular term(stress intensity factor) is determined by the variational method for multi-regions.The computation results show a satistactory convergency of the stress intensity factors and the calculation is very time-saving.