Abstract: This paper deals with the aaisymmetrical deformation of shallow shells in large deflection, which are in conjunction with linear elastic structures at the boundary. A method of mired boundary condition for this problem is introduced, then the problem of a composite structure is transformed into a problem of a sinlgle structure and the integral equatiaus are given, The perturbation method is used to obtain the solutions and an eaemple of composite structure consisting of a shallow spherical and a cylindrical shell is presented.