Energy dissipation due to sloshing liquid in rigid torus shaped containers is studied using the potential flow model in conjunction with the boundary layer correction. The analysis is based on the perturbation method to solve for the nonlinear free surface equation. Special consideration is given to the case of resonant interactions which yield interesting damping characteristics. The results suggest that large diameter ratios and low liquid heights lead to efficient damper design. The concept is applicable to a wide spectrum of problems characterized by low frequency oscillations as encountered in wind, ocean and earthquake engineering.