The objective of the paper is to apply modern numerical techniques of nonlinear dynamics to the problem of control of the roll motion employing U-shaped anti rolling tanks (ART). Parametric rolling in head seas is the focus of the paper. A transom stern small vessel, well known for her tendency to develop strong parametric excitation is investigated. Nonlinear equations are employed to describe the liquid motion inside the tank, the forces and moments generated by the tank on the ship and the coupled ship motions (heave, roll and pitch). These are numerically solved for different initial conditions. An analysis of the dynamical behavior of the vessel with stabilization is presented in the form of numerical limits of stability, safe basins, integrity curves and integrity surfaces. Finally, curves of critical amplitude for different wave tunings are computed. A design procedure for quantitative assessment of the level of parametric rolling mitigation by means of ART's is discussed. Copyright