Abstract The scaled boundary finite element method (SBFEM) is a novel semianalytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. Assuming ideal and irrotational flow and small-amplitude free-surface elevation, this paper aims at developing the proposed method combining a modal approach for the sloshing problems in horizontal elliptical tanks with baffles under horizontal excitations. Firstly, based on Laplace equation and SBFEM coordination systems, the derivations for the eigenvalue problem by using the scaled boundary finite element method under zero external excitation and solutions of SBFEM equations are expressed in details, then the natural mode shapes of sloshing and their corresponding frequencies are can be obtained. The SBFEM needs discretize only the water surface and walls with curved surface finite-elements and keeps the radial differential equation solved completely analytically. Subsequently, based on an appropriate decomposition, an efficient methodology is proposed for externallyinduced sloshing through the calculation of the corresponding sloshing (or convective) masses. In comparison with analytic solution method and other numerical methods, numerical results show that the proposed method can produce more accurate solution than the conventional numerical methods with far less number of degrees of freedom. Meanwhile, the effects of the vertical baffles on the hydrodynamic pressure mode shapes, sloshing flows and sloshing masses are examined in details.