  In this paper we consider the stability issue for the inverse problem of
determining an unknown inclusion contained in an elastic body by all the pairs
of measurements of displacement and traction taken at the boundary of the body.
Both the body and the inclusion are made by inhomogeneous linearly elastic
isotropic material. Under mild a priori assumptions about the smoothness of the
inclusion and the regularity of the coefficients, we show that the logarithmic
stability estimate proved in \cite{ADiCMR14} in the case of piecewise constant
coefficients continues to hold in the inhomogeneous case. We introduce new
arguments which allow to simplify some technical aspects of the proof given in
\cite{ADiCMR14}.
