High rise building structures are both a necessity and a matter of sophistication and pride for structural engineers. Forces of nature in the form of earthquakes and cyclones starts playing brutal games with the structures, higher the structure goes, and higher it attracts the forces and wrath of nature in the form of seismic force. Seismic force, predominantly being an inertia force depends on the mass of the structure causing requirement of heavier sections as mass increases. And these heavy sections further increase the mass of the structure leading to even heavier seismic forces. Structural designers are met with the huge challenge to balance these contradictory physical phenomena to make the structure safe. The structure no more can afford to be rigid. In recent year, it is common practice to install vibration control devices on structures to mitigate their dynamic response caused by different factors, mainly due to wind and earthquake excitations. Among these devices, tuned mass dampers (TMD) have been widely used in building to mitigate dynamic responses of buildings. As the structural complexity of buildings increase, their response to such excitations may become more prone to torsional motion. Torsional motion induced by such excitations can be suppressed by utilizing TMDs. The performance of TMD at different positions are important for torsionally coupled structures. In this study, the performance of bi-directional tuned mass dampers (BTMD) in reducing the torsional response of a building under bi-directional earthquake excitations was studied and evaluated.