AT‐matrix formalism is presented for a multilayered three‐dimensional scatterer of arbitrary shape immersed in a fluid, to study the scattering of acoustic waves. The layers of the scatterer may be composed of elastic or viscoelastic material. Explicit expressions for theT‐matrix of a two‐ and three‐layered scatterers are presented. Frequency dependent numerical results have been obtained for two‐layered prolate and oblate elastic and viscoelastic spheroidal obstacles where the inner layer is assumed to be a cavity. The differential, backscattering, absorption, and extinction cross sections have been obtained for both thin and thick layers. For purposes of comparison, results for the homogeneous scatterers are also presented. The scattering cross sections for a thick outer layer are found to be considerably different from those for a thin layer.