Tuned liquid dampers (TLDs) are among the most economical and effective passive damping devices. They have been increasingly used to reduce dynamic response and protect structures from failure due to external dynamic excitations. Slat screens are one of the most effective devices used to increase the inherent damping of a TLD, and to reduce the non‐linearity of the free surface motion. A numerical algorithm has been developed to solve the complete non‐linear, moving boundary flow problem in a TLD outfitted with slat screens. The model has been developed to handle conditions leading from small to large interfacial deformations without imposing any linearization assumptions. The numerical algorithm is based on the finite‐difference method. The free surface has been determined using the volume‐of‐fluid method and the donor–acceptor algorithm. The effect of the slat screens has been modeled explicitly by using the partial‐cell treatment method. The present algorithm has been validated against experimental data. The results indicated that the present algorithm is capable of providing accurate details of the flow field inside the TLD and through the screens. These details are essential to improve our understanding of the important parameters governing the performance of a TLD, and hence, to enhance our ability to design better TLDs. Copyright © 2010 John Wiley & Sons, Ltd.