<p>Ground-borne vibrations induced by dynamic loads pose significant risks to the performance and safety of multi-story structures. Trenches are commonly used as passive or active isolation systems, yet their effectiveness strongly depends on geometry, location, and infill material. This study presents a comprehensive parametric investigation into the effects of open and infilled trenches on the dynamic responses of multi-story structures subjected to point and earthquake loads. A two-dimensional (2D) finite element-infinite element (FE-IE) model was developed in the Laplace domain, incorporating soil-structure-trench interaction (SSTI) and wave radiation into unbounded soil. The numerical formulations were implemented in FORTRAN 90 programming language, and the model was validated against benchmark problems before being applied to parametric case studies. Different trench depths, distances, and infill conditions ranging from soft geofoam to rigid materials were examined. Results indicate that open trenches near the structure effectively mitigate vibrations from point loads but amplify responses under earthquake excitations. In contrast, rigid material-infilled trenches, when placed at an adequate distance, significantly reduce displacement and stress responses for both loading cases, highlighting their potential as efficient wave barriers. Under point loading, rigid material-infilled trenches reduced maximum displacements by nearly 27% at both the top and base of the structure compared to open trench conditions. Under earthquake excitation, the reduction was slightly smaller but still significant, with displacements decreasing by about 48% when rigid barriers were used.</p>