The object of this study is to design radar absorbing structures (RAS) with load-bearing ability in the X-band. Glass/epoxy plain-weave composites of excellent specific stiffness and strength, containing multi-walled carbon nanotubes (MWNT) to induce dielectric loss, were fabricated. Observations of the microstructure and the permittivity of the composites confirmed that the fabrics are suitable for use as RASs. A genetic algorithm and a theory of the reflection/transmission of electromagnetic waves in a multi-layered RAS were applied to design an optimal RAS composed of MWNT-filled composites. The thickness per ply was observed to vary, depending on the number of plies and the MWNT contents. A fabrication process was proposed that considered the variation. The proposed process was in the fabrication of a designed RAS, and the theoretical and measured reflection losses of the RAS were found to be in good agreement.