Abstract-Composites containing conducting inclusions are required in many engineering applications, especially, for the design of microwave shielding enclosures to ensure electromagnetic compatibility and electromagnetic immunity. Herein, multilayer shielding structures are studied, with both absorbing and reflecting composite layers. In this paper, fiber-filled composites are considered. For modeling absorbing composites with low concentration of conducting cylindrical inclusions (below the percolation threshold), the Maxwell Garnett theory is used. For reflecting layers, when concentration of inclusions is close to or above the percolation threshold, the McLachlan formulation is used. Frequency dependencies for an effective permittivity are approximated by the Debye curves using a curve-fitting procedure, in particular, a genetic algorithm.