A method for the analysis of the free vibrations of a circular cylindrical shell with a longitudinal, interior plate is developed. This method is based on the extended Rayleigh-Ritz technique. Separate displacement functions are assumed for the shell and plate. Constraint equations are used to enforce displacement compatibility between the plate and shell. The importance of including the in-plane degrees of freedom of the plate in the analysis is investigated. Studies are made to determine the effects on the system frequencies and modes of rigid and hinged joints between the plate and shell and the location of the plate. In general, the effect of the joint condition and plate location on the frequencies varies for different modes. The fundamental mode of the partitioned shell involves predominantly bending of the plate unless the plate is very thick. The effect of the joint condition on the frequency depends on the character of the mode, although the frequencies are higher when the joint is rigid than when it is hinged. The fundamental frequency increases as the plate is located farther from the center of the shell, but higher frequencies show a less predictable behavior.