This paper concerns the treatment of swing dynamics in a power grid using a continuous approach. Rather than addressing the problem as oscillations in a discrete system, we model the swing dynamics as a propagating electro-mechanical wave using a partial differential equation. A ring geometry with a one-dimensional wave equation is used to analyze the underlying dynamics. A control method is proposed to damp the system dynamics using the concept of Interior Wave Suppression. Unlikedomains withboundaries such as strings, any concentrated input to the ring generates waves in two directions, thereby preventing total absorption. Using a judicious combination of concentrated control inputs, it is shown that a near unidirectional wave can be generated, with minimal backwaves. The resulting closed-loop system is proved to be stable. The overall modeling and control methods are shown to be implementable in a power grid using phasor measurement units as sensors and flexible ac transmission system devices, such as thyristor controlled series compensator, as actuators. How, the proposed methods of modeling and control can be applied to a network of rings is briefly discussed. Numerical simulations are carried out to validate the theoretical derivations.