Power flow between source and passive receiver structures is a common metric for characterizing the dynamics of coupled structures. The objective is generally to reduce the amount of power flow between the structures by means of structural modifications, insofar as to reduce the overall levels of vibration of the coupled system. As such, the sensitivity of power flow to changes in inertial, elastic, and dissipative properties of the structure is quantified. It is shown that power flow into a receiver is not always directly proportional to the amount of damping in the receiver, but is also dependent on the amount of damping present in the source at a given frequency. The sign of the sensitivity can provide information as to when a change in damping will increase or decrease power flow; positive indicates an increase in power flow, negative indicates a decrease. A similar analysis is performed on modifications made to a structure’s mass and stiffness properties. Relationships between power flow and power flow sensitivity are shown for a simple single degree of freedom source-receiver coupling, and is extended to a multi-degree of freedom coupling between two beam structures.