Color‐coded and vector‐arrow grid representations of the Poynting vector field are used to show the energy flow in and around a fluid‐loaded elastic cylindrical shell for both forward‐ and backward‐propagating waves. The present work uses a method adapted from a simpler technique due to Kaduchak and Marston [G. Kaduchak and P. L. Marston, ‘‘Traveling‐wave decomposition of surface displacements associated with scattering by a cylindrical shell: Numerical evaluation displaying guided forward and backward wave properties,’’ J. Acoust. Soc. Am. 98, 3501–3507 (1995)] to isolate unidirectional energy flows.