In this study, a band-stop Frequency Selective Surface (FSS) was designed for a 5GHz frequency band. 2.4GHz, 3.6GHz, 4.9GHz, 5GHz and 5.9GHz frequency bands are the WLAN channels specified in IEEE 802.11 protocol. The devices are often used at 2.4GHz. But in most cases, this frequency cannot be used efficiently due to limited number of channels and excessive number of devices operating at this frequency. This drawback can be eliminated by using 5GHz frequency. Effective usage can be achieved because of the few numbers of equipments operating and many channels available in this frequency band. In this context, a FSS band stop filter was designed to prevent interference and block undesired waves within 5GHz frequency bands. Parameters such as FSS geometry, its period, the element type used, distance between the arrays, parameters of the medium, angle of incidence and polarization of the incident wave are important in FSS design. The shielding effect of the FSS in a 5GHz frequency band was examined by using Green's Functions and the Method of Moments (MoM). Square type patch elements were used in filter design. The FSS design was also tested under vertical polarization for various length and numbers of square patches. Best shielding effect was obtained under vertical polarization with theta = 0 degrees and theta= 30 degrees for a FSS design having 1 square patch. The FSS design for various numbers of square patch elements was also tested. Four different designs composed of 1, 4, 9 and 16 square patches acted as a stable filter in the 5GHz frequency band in vertical polarization for theta = 0 degrees and phi = 0 degrees. Undesired propagations were also low. This value indicates that the design is successful as a filter structure. The best shielding effectiveness was obtained for 1 square patch FSS design in vertical polarization at theta = 30 degrees. As the patch number increases some undesired propagations were observed between 11GHz and 12GHz. Especially for 9 square patch FSS design, at 11GHz frequency a 22dB undesired propagation was observed. This case shows that the FSS filters act also at 11GHz frequency which is undesirable.