Viscous fluid dampers are often incorporated into structures without much consideration for the inherent elastic flexibility of the damper sub-system and associated connections. However, this damper sub-system flexibility can alter the phasing of damper and structural forces and influence the overall structural response. This paper investigates how damper sub-system stiffness affects the overall displacement response and total system force of a structural system in a seismic event. The single-degree-of-freedom (SDOF) model consists of an elastic structural element, a viscous damper and an elastic spring that represents the damper sub-system flexibility. This model is subject to ground motion acceleration excitations. Results from ground motion simulations indicate that if a damper is designed assuming a rigid sub-system, the median peak displacement response can be up to 33% higher than expected, depending on the level of added supplemental damping, the damper sub-system stiffness, and the period of vibration of the structural system. For this reason, it is recommended that in order to limit the impact of phasing effects, designers should ensure that the damper sub-system stiffness is five to ten times the stiffness of the main lateral load resisting system.