The analytical formulation for the total scattering cross section of a cylindrical cavity in an elastic medium is given for the case of inclusion of compressional and shear wave attenuations. Examples are computed of relatively small attenuations exemplified by the material polymethacrylate and relatively large attenuations exemplified by polyethylene. The inclusion of wave attenuations known to exist in these materials cause the scattering cross section to diminish significantly for wave‐number cylindrical‐cavity‐radius product up to 10.