The elastic strain energy of a misfitted coherent inclusion is discuss
ed using the Eshelby method for ellipsoidal inclusions. Deviatoric and
tetragonal misfit strains in an elastically inhomogeneous spheroidal
inclusion are particularly considered. The variation of the elastic st
rain energy is evaluated as a function of the shape and orientation of
the inclusion. Results obtained are compared with these for a coheren
t inclusion with purely dilatational misfit strains. Under certain dev
iatoric misfit strains and elastic moduli of the inclusion, the least
elastic strain energy is achieved by a spheroid with an intermediate s
hape between a plate and a sphere or between a sphere and a needle.