This paper reports results of the structural response of empty steel tanks under vertical ground motions. The tanks are modeled using a finite element discretization using shell elements, and the vertical motion is applied and analyzed using nonlinear dynamics. Several excitation frequencies are considered, with emphasis on those that may lead to resonance of the roof. The computational results illustrate that as the base motion frequency is tuned with the frequency of the first roof-mode of the tank, the system displays large-amplitude displacements. For frequencies away from such mode, small amplitude displacements are obtained. The effect of the height of the cylinder on the dynamic response of the tank to vertical ground motion has also been investigated. The vertical acceleration of the ground motion that induces significant changes in the stiffness of the tank was found to be almost constant regardless of the height of the cylinder.