Implementation of supplemental damping systems (e.g., the dynamic vibration absorbers (DVAs)) to mitigate excessive tall building vibrations induced by external dynamic loads (wind storms or earthquakes) has increased over the last several decades. A tuned liquid damper (TLD) is a specific type of the DVAs that consists of a rigid tank which is partially filled with a liquid, usually water. The sloshing liquid inside the tank provides inertia forces that counteract the forces acting on the structure, thus reducing the building motion. A single sway mode of vibration is usually targeted, however, for certain structures multiple modes may need to be suppressed. Moreover, the location of the TLD on the floor plate is important for certain modes, such as a torsionally dominate mode. In this paper, a three-dimensional (3D) finite element (FE) structure-TLD system model (3D-structure-TLD) is proposed where the TLDs can be positioned at any location on the structure allowing the most effective positions in reducing the structure's dynamic response to be determined. Therefore, the response of a 3D structure (tower, high-rise building, bridge, etc.) fitted with single or multiple TLD(s) and subjected to dynamic excitation can be predicted using the proposed FE model. For torsionally sensitive structure (eccentric/irregular structures), this type of 3D numerical analysis is highly recommended. Two nonlinear TLD models are employed to simulate the TLD and implemented in the FE model. The 3D-structure-TLD system model is validated for the cases of sinusoidal and random excitation forces using existing experimental test values. Results from the 3D-structure-TLD system model are found to be in excellent agreement with values obtained from experimental tests.