Theoretical solutions are presented for the dynamic stability of liquid-filled cylindrical shells under vertical excitation. For the motion of the shell, the modified Galerkin method is applied to the dynamic version of the Donnell basic equation ; while, for the motion of the liquid, the velocity potential of the liquid is used so as to satisfy the boundary conditions. The equation of motions coupled with both the shell and the liquid are derived from a type of coupled Mathieu's equations. The instability boundaries at which parametric resonance occurs are determined using Hsu's method. The validity of the theoretical analysis was confirmed through precise experiments using the polyester test cylinder and water. As a result, it was found that a principal instability resonance and a combination instability resonance of the sum type of two natural vibrations, each of which has the same circumferential wave number and different axial mode of vibration, are likely to occur.