Presented here is a dynamic analysis of a multiply connected body for magnetic resonance elastography. We derive, from first principles, the closed form solution to a concentric cylindrical body undergoing harmonic oscillations. We then describe the phantom construction, experimental procedure, parameter estimation, and the forward problem. To validate our model, we use the shear moduli estimates as inputs to solve the forward problem with a finite-element model (FEM) and compare that with experimental results. Finally we consider the immediate consequences of this work as well its implications for future research.