The resonant behavior of a cylindrical microwave cavity partially filled with a cold plasma of arbitrarily large density is studied theoretically and experimentally. Curves showing the resonant frequencies as functions of the plasma density are given for the lower order modes. The modes are generally not pure TE or TM modes but are of hybrid character. In addition to the modes that are related to those of the empty cavity, there is a class of modes of surface wave character that do not exist in the empty cavity. Experiments have been performed and are generally in agreement with the theory. However, for some modes great discrepancies are observed. These correspond to the unexplained additional resonances obtained in plasma resonance experiments.