The problem of the elastic buckling of a cylindrical liquid-storage tank subject to horizontal earthquake loading is considered. An equivalent static loading is used to represent the dynamic effect. A theoretical solution based on the nonlinear Fl$ddot{u}$gge shell equations is developed, and numerical results are found using the new differential quadrature method. A second solution is obtained using the finite element package ADINA. A major motivation of the study was to show that the new method can serve to verify finite element solutions for cylindrical shell buckling problems. For this purpose the paper concludes with a comparison of buckling results for a number of cases covering a wide range in tank geometry.