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A solution for reducing the radar cross section (RCS) of a microstrip antenna based on the use of frequency selective surfaces (FSSs) is described. The goal is accomplished by replacing the solid ground plane of the device with a hybrid structure comprising a suitable FSS. The behavior of the hybrid ground plane illuminated by a plane wave is analyzed by using a periodic method of moments (PMM), and it is modeled by resorting to a transmission-line equivalent circuit. Similarly, the propagation of the quasi-TEM mode along the modified feeding line of the array is represented by an equivalent circuit for surface waves. The two simplified analyses provide useful design criteria for the hybrid ground structure. The presented solution guarantees a decrease of the out-of-band radar signature of the target while preserving the desired in-band radiation characteristics of the low-profile array. A careful comparison to alternative configurations employing different ground planes has revealed the superior performance of the proposed design. Measurements on a realized prototype show a good agreement with simulations and prove the reliability of the design approach.