Hyperboloidal reinforced-concrete shells are modeled using orthotropic quadrilateral flat plate finite elements. The supporting columns and top ring-beam are modeled by beam finite elements. Natural frequencies and corresponding mode shapes are found for several different tower configurations. Results for fixed-base shells are in close agreement with those determined using alternate methods of analysis. A cooling tower in the 1200 MW Fossile Fuel Steam Generating Power Plant at Paradise, Kentucky (Tennessee Valley Authority) is studied. Time-history responses of 30 sec to the North-South component of the 1940 El Centre earthquake are computed by the technique of modal superposition. Only the modes with one circumferential wave are excitable by horizontal motion. Contributions of the first three such modes are found using response spectrum analysis. The effect of viscous damping is considered. Two different structural programs, NASTRAN and SAP IV, are used in different portions of the solution process. Advantages, disadvantages, and limitations in the present application are discussed.