An analytical model of a partly-filled tank of arbitrary cross-section is developed for predicting transient lateral slosh force and overturning moment using linear slosh theory. Slosh frequencies and mode shapes are initially estimated using the variational method, which is applied to the linearized free-surface boundary condition. The resulting truncated system of linear ordinary differential equations is subsequently solved numerically to determine the fluid velocity potentials followed by hydrodynamic force and moment. The validity of the model is examined through comparisons with available analytical solutions and experimental data. The slosh force and roll moment are obtained for four different tank cross-sections, namely, circular, elliptical, modified-oval and Reuleaux-triangle. It is shown that the magnitudes of the slosh force and overturning moment are strongly dependent upon the tank cross-section. The slosh model is subsequently integrated to a roll plane model of an articulated tank-semitrailer vehicle to study the effect of dynamic liquid slosh as well as the tank cross-section on the steady-turning roll stability limit of the vehicle under constant and variable cargo load conditions. The results suggest that a tank cross-section with lower overall center of mass and lower critical slosh length yields an enhanced roll stability limit under medium- and high-fill conditions. •An analytical model of lateral slosh is developed using the linear slosh theory.•The model is applicable to tanks with arbitrary cross-sections and liquid depths.•Effectiveness of Reuleaux-triangle tank in suppressing the liquid slosh is shown.•Rollover limits are much lower than those of the widely-used quasi-static analysis.•Highest rollover limits are obtained for vehicle with the Reuleaux-triangle tank.