  We consider the double layer potential (Neumann-Poincar\'e) operator
appearing in 3-dimensional elasticity. We show that the recent result about the
polynomial compactness of this operator for the case of a homogeneous media
follows without additional calculations from previous considerations by
Agranovich et.al., based upon pseudodifferential operators. Further on, we
define the NP operator for the case of a nonhomogeneous isotropic media and
show that its properties depend crucially on the character of non-homogeneity.
If the Lam\'e parameters are constant along the boundary, the NP operator is
still polynomially compact. On the other hand, if these parameters are not
constant, two or more intervals of continuous spectrum may appear, so the NP
operator ceases to be polynomially compact. However, after a certain
modification, it becomes polynomially compact again. Finally, we evaluate the
rate of convergence of discrete eigenvalues of the NP operator to the tips of
the essential spectrum.
