The vibration of a large tank caused by an explosion that occurs at a place apart from the tank is analyzed. Because the tank is double-walled and the liquid is contained in the inner shell, the vibration of the outer shell subjected to the explosion-induced pressure wave that travels outside the tank is analyzed without considering the liquid. A cylindrical tank with a spherical roof is considered as a realistic three-dimensional (3D) model, and a computationally efficient semi-analytical method that is applicable to the 3D geometry of the tank–fluid interface is investigated. First, cylindrical coordinates are introduced such that the longitudinal axis intersects the center of the tank base and is normal to the explosion source plane, thereby defining the inner and outer radii of the analysis domain of the fluid motion. Next, the solutions are expressed in terms of coordinate-dependent eigenvalues and a reduced order model is developed by applying the Galerkin method to the governing equations that take into account the compressibility and nonlinearity of the fluid motion. The method is verified by comparing with earlier results obtained by a numerical method. We also analyze the vibration of the tank shell by developing its finite element (FE) model and transforming the model into modal equations to develop a reduced order model for the fluid–tank system.