In this paper, a simple synthesis technique to obtain the geometrical parameters of the modified circular ring for angular and polarizations (perpendicular and parallel) stable frequency selective surface (FSS) has been discussed. The geometrical parameters of the modified circular ring FSS structure have been achieved using the proposed synthesis technique, which is based on the equivalent circuit (EC) approach. In addition to this, the numerical analysis is also discussed to determine the values of EC parameters, which depends on the basic system level characteristics such as frequency of operation and reflection/transmission coefficients. The analytical results are supported using the full-wave three-dimensional electromagnetic (EM) simulators such as CST Microwave Studio and Ansoft HFSS. The sensitivity of the structure to the perpendicular and parallel polarized EM wave up to 50° angle-of-incidences (AOIs) has been discussed. The stability over different AOI is attributed to the appropriate thickness of the structure with its small unit-cell dimensions. We have also fabricated and experimentally tested the proposed FSS structure.