<p>Multi-storey buildings often experience significant vibrations due to their flexible nature and exposure to earthquake and wind loads. These vibrations can affect structural safety and serviceability. Passive vibration control systems are commonly used due to their simple design and reliable performance. However, traditional tuned mass dampers have limitations related to the requirement of additional mass. Tuned inerter dampers provide an alternative solution by producing high inertial forces without adding much physical mass. This study examines how a nine degree of freedom shear building responds to vibrations when a tuned inerter damper is used. The building is subjected to base excitation, and its dynamic behaviour is examined through frequency-domain analysis. The damper is placed at the bottom and top storeys to study the effect of installation location. The influence of different inertance ratios on the structural response is also examined. The performance of the system is evaluated using normalized maximum displacement and inter-storey drift. The results show that placing the damper at the bottom storey gives a noticeable reduction in displacement and drift, even for small inertance ratios. On the other hand, when the damper is installed at the top storey, higher inertance values are required to obtain meaningful vibration reduction. The results show that the position of the damper and the inertance ratio are both important for controlling vibrations in a multi degree of freedom building.</p>