Seismic demand can be reduced by modifying the structural response of the system. Viscous dampers are an effective passive control device for reducing vibrations in building structures. The present study investigates the performance of linear viscous dampers in vibration control of multi-storey building structures under seismic excitation considering the effect of soil flexibility. Six-storey steel 3D framed buildings with three different building plans, namely symmetric, T and L shapes, are modeled using SAP 2000. Soil type I (hard) and type II (medium) are considered as per IS 1893:2002 to incorporate the effect of soil flexibility by using springs at supports for medium type soil and fixed supports for hard soil. The spring constants are obtained from Gazetas’ equations. To measure the control performance, inter-storey drift and maximum top displacement are considered as objective functions. Linear time history simulation is performed using white noise (ensuring wider frequency content) to quantify the objective functions. After performing the analysis and comparing with the uncontrolled case for both hard and medium soil, it is observed that maximum reduction in inter-storey drift and average top displacement can be obtained. Eccentric plans have larger uncontrolled values than the symmetric plans, thus additional design criteria to be followed when opting for eccentric plans. The study reveals that application of supplemental viscous dampers results in greater control of vibrations in such plans. Vibration control of viscous damper is comparatively better in hard soil than in medium type soil.