The sound fields resulting from a plane wave incident on a spherical elastic shell are found. Both the internal and external fields due to the shell are considered and compared with well‐known results. The Rayleigh limit is discussed, and it is found that the external field is similar to that produced by a rigid sphere but with more complicated coefficients. The internal field is of a complicated nature but reasonable to consider for numerical computation. The sound fields for a hemispherical shell mounted on a rigid medium are obtained by the image method. Numerical results for the sound intensity at the center of the hemisphere are presented for various elastic materials.