Abstract: The sloshing response of a liquid in a cylindrical tank with an arbitrary cross-section under lateral excitations was studied by the semi-analytical method. Based on the superposition principle, the velocity potential function of forced vibration was assumed to be the sum of the rigid potential and the liquid perturbed potential. The rigid part was obtained using a nonhomogeneous boundary condition. Following the mode superposition method, the liquid perturbed part was expressed at the generalized coordinates with unknown time variable coefficients. Substituting the total velocity potential into the free surface wave condition, the dynamic response equation was established by orthogonality of modes. The results show excellent agreement with those obtained by the finite element method.