As a fundamental research problem relating to the amplitude of Pogo oscillation of liquid propellant launch vehicles, an experimental study was conducted in which a cylindrical shell vertically hung and partially filled with liquid was longitudinally excited at the bottom in the authors' previous paper. The vibration of the shell wall was induced at the several specific ranges of exciting frequency by the mechanism of parametric excitation. To analyze this problem, a set of nonlinear equations of vibration is derived with the aid of the finite element method. Axial mode shapes of the axisymmetrical and circumferentially n-wave modes are calculated from the linear part of the set of nonlinear equations. Using these two modes, the set of nonlinear equations is reduced to the coupled equations of two degrees of freedom. The equations to calculate a stationary vibration, and its stability are derived. The range of the parametric excitation is obtained in the plane of exciting force amplitude and frequency.