  We consider the Neumann-Poincar'e (double layer potential) operator in 3D
elasicity on a smooth closed surface. Its essential spectrum consists of 3
points. We find the asymptotics of sequences of eigenvalues converging to these
three pounts. They are expressed via the eigenvalue distribution for a matrix
eigenvalue problem depending on the points of the cotangent bundle of the
surface. For the two-sided asymptotics for the distribution of the the union of
sequences of eigenvalues converging to the point of the essential spectrum from
both sides, an expression is found via the Euler characteristics and the
Willmore energy of the surface.
