Abstract: Analytical method to the chain of identical substructures is treated in this paper. The nalysis can also be applied to the semi-analytical method in the mathematical physics, that is to make discretization to the transverse cross section and then solve the differential equations along the longitudinal direction. Two methods are treated concurrently, i.e. the method of shifting invariance and the method of initial parameters and transfer matrices. The mutual relation between these two methods is explained. T...