Abstract The effects of surface-piercing or bottom-mounted vertical baffles on two-dimensional liquid sloshing characteristics in a half-full non-deformable horizontal cylindrical container of elliptical cross section is investigated. The problem solution is achieved by employing the linear potential theory in conjunction with the successive conformal transformation technique, leading to matrix eigenvalue problems on simple (rectangular and semi-infinite strip) regions. Plots of the resonant eigen-frequencies as a function of the baffle extension at selected container aspect ratios are presented and discussed for the three lowest antisymmetric and symmetric transverse oscillation modes. Also, the effects of vertical baffles on the hydrodynamic pressure mode shapes and sloshing flows are examined through appropriate 2D images. The surface-piercing vertical baffle is demonstrated to be an effective tool in reducing the antisymmetric sloshing frequencies, especially for lower aspect ratio tanks and higher modes. On the other hand, the bottom-mounted baffle is shown to have a great influence on the higher antisymmetric slosh modes only when its tip approaches the liquid free surface. Limiting cases are considered and good agreements with available analytic and numerical solutions as well as experimental data are obtained.