Static eccentricity (SE) is an intrinsic fault existing in both faulty and newly made resolvers. The late diagnosis of SE causes severe damages to mechanical parts of resolver such as bearings, cores and even windings, in addition to wrong position estimation. However, so far fault diagnosis has not been investigated for any Resolver. In this paper, SE fault diagnosis is discussed for a sample wound-rotor (WR) cylindrical resolver. Time stepping finite element method (TSFEM) is used to simulate the resolver, and its accuracy is validated by a comparison between the results of simulation and experimental tests. Then, some fault indices are defined to diagnose the SE fault occurrence, and its magnitude is predicted using Fast Fourier transform (FFT). Finally, to ensure that indices are unique, the performance of the studied resolver is evaluated under other types of faults including Dynamic Eccentricity (DE) and Short-circuit (SC) that may excite the same indices.