The deformed cylinder method (DCM) is a very versatile model that can be used on a wide range of acoustic scattering problems. To date, it has been applied to uncoated axisymmetric bodies of circular cross section, whether they be rigid, elastic solids, or shells. In this article, the method is applied to three bodies that are covered to varying degrees by a viscoelastic absorbing layer. These bodies include a coated spheroidal shell, a spheroidal shell partially covered with an axisymmetric coated band, and a cylindrical shell with a lengthwise coated strip. For the coated spheroidal shell, the effects of varying coating thickness and coating loss on the scattering are examined. Results indicate that the coating has little effect below 2 kHz, but above this level, the target strength decreases with increase in either thickness or loss. At the higher frequencies, the analytical solution used in the DCM becomes unstable. To overcome this, a high‐frequency solution is obtained by combining the DCM together with the physical optics method and layered plate theory. This high‐ frequency solution can also be used in situations where the shape of a partial coating is of a form that prohibits the analytical solution from being used. This was the case with the cylindrical shell with the lengthwise strip.