ICF conceptual designs have been proposed in which flexible tubes conveying liquid metal are subjected to repetitive impulsive pressures. Because the tubes are vertical, very long and carry liquid metal, gravity gradient effects are substantial. The complete equation of motion is presented. Results are obtained for the vibrational mode shapes and corresponding frequencies of the tubes. It is shown that the gravity gradients can produce strong asymmetries in the mode shapes and shifts in the numerical values of the natural frequencies. Results of an approximate perturbation analysis are also presented to support the exact solution.