A theory is presented for the determination of the free vibration characteristics of vertical, thin, circular cylindrical shells, partially or completely filled with stationary liquid. The shell may be uniform or non-uniform, provided it is axially symmetric. This is a finite-element theory, using cylindrical finite elements, but the displacement functions are determined by using classical shell theory. The inertial loading of the fluid is taken into account by incorporating the virtual mass of the fluid into the mass matrix of those finite elements which are below the liquid free-surface. Calculations of the natural frequencies and eigenvectors were conducted for one such shell, for which experimental data were available. Agreement between theory and experiment was found to be quite good.