A plane wave excitation of a periodic conducting patch-array embedded in an infinite multilayered dielectric cylinder, as a shielding structure, has been studied. Based on the Green's functions, the integral equation is formulated for describing the current on a conducting patch-array. Using Galerkin's method, the surface currents on the conducting patches are expanded in the form of series weighted Chebyshev polynomials of the first kind and the unknown coefficients are obtained by solving a resultant system of linear equations. The validity of the formulation and the accuracy of the numerical solution are demonstrated for different array geometries. The numerical results depict the penetrated field, the scattered field and the shielding effectiveness for four different array geometries. Some of these results are compared to the simulated results using Zeland Fidelity Workshop (ZFW), and a good agreement was achieved