This dissertation presents a comprehensive study of the dynamic response of storage tanks containing high-level radioactive wastes in nuclear facilities. Of the many issues that are peculiar to these systems, four important ones have been studied. Accordingly, the study is presented in four parts. The first part deals with the dynamic response of flexible tanks that are placed inside concrete vaults and are attached to the vaults both at the top and the bottom. The tanks are presumed to be fixed at the base and supported by either a roller or a hinge at the top. The response quantities examined include the natural frequencies of vibration, the hydrodynamic pressures and the induced tank forces. The general trends are established by comparing the response quantities for the top-constrained systems with those for base-excited cantilever systems. The second part deals with the response of rigid and flexible tanks containing stratified liquids. The liquid is considered to be arranged in layers with varying layer thicknesses and mass densities, or to be inhomogeneous with a continuously varying mass density. In addition to the free vibrational sloshing characteristics of the liquid, the responses examined include the vertical displacements at the free surface, and the impulsive and convective components of the hydrodynamic wall pressures and associated tank forces. A simplified analytical procedure that estimates the response quantities for the layered systems from corresponding solutions for homogeneous systems is also presented. The third part presents an exploratory study for assessing the effects of tank-base flexibility on the response of vertically excited liquid storage tanks. A suitable model of the tank-liquid-foundation-soil system is considered, and the natural frequencies, the associated damping ratios and the induced pressures are studied for a wide range of base-flexibility values. The final part estimates the effects induced by the impact of the sloshing liquid on the tank roof. Consideration is given not only to the effects that are induced on the roof but also to the effects that are transferred to the side-wall. Both rectangular and cylindrical systems are considered and the effect of changing the slope of the roof on the induced impact effects is also studied.