Abstract.  New matching theory is proposed for stability analysis of Resistive Wall Modes (RWMs) in rotating plasmas. It is found that for rotating plasmas, the classical asymptotic matching theory becomes invalid in principle. The matching problem should be generalized to use inner layers with finite width to overcome the difficulty that a resonant surface, which exists somewhere in finite distance apart from the rational surface depending on the unknown rotation frequency of the RWM, should be included in the layers. For the first time, numerical analysis based on the generalized matching problem shows that the location of resonance determined by rotation in the inner layer significantly affects the stability of RWMs. Analytic theory for the generalized matching problem is developed to interpret the results by generalized matching problem and to search the unknown location of the resonant surface.