Abstract: The governing equations of laminate faced sandwich cylindrical shallow shells based on the first order shear theory with large deflection are high order partial differential equations. Four dependent functions are involved. They are the deflection w, the rotations of the normal to the undeformed median surface Φx, Φy and the force function F. In the present paper these dependent functions are expressed as generalized double Fourier series with beam eigenfunctions as general terms. These series are chosen so that various boundary conditions are satisfied. By substituting these expressions into the high order partial differential governing equations, they become a set of algebraic equations. Here is developed a universal and effective method to solve the problems on the shear theory of laminated or sandwich thin walled structures with large deflection.