The tuned liquid damper (TLD) is a system used to reduce the response of tall structures. Numerical modeling is a very important tool when designing TLDs. Many existing numerical models are capable of accurately capturing the structure–TLD system response at serviceability levels, covering the range where TLDs are primarily intended to perform. However, these models often have convergence issues when considering more extreme structural excitations. The goal of this study is to develop a structure–TLD model without convergence limitations at large amplitude excitations. A structure–TLD numerical model where the TLD is represented by a two-dimensional incompressible smoothed particle hydrodynamics (ISPH) scheme is presented. The TLD contains damping screens which are represented by a force term based on the Morison equation. The performance of the model is assessed by comparing to experimental data for a structure–TLD system undergoing large amplitude excitations consisting of 4-h random signals and shorter transient signals. The model shows very good agreement with the experimental data for the structural response. The free surface response of the TLD is captured accurately by the model for the lower excitation forces considered, however as the excitation force is increased there are some discrepancies. The large amplitude excitations also result in smoothed particle hydrodynamics (SPH) fluid particles penetrating the boundaries, resulting in degradation of the model performance over the 4-h simulations. Overall, the model is shown to capture the response of a structure–TLD system undergoing large amplitude excitations well.