  Eisenstein classes of Siegel varieties are motivic cohomology classes defined
as pull-backs by torsion sections of the polylogarithm prosheaf on the
universal abelian scheme. By reduction to the Hilbert-Blumenthal case, we prove
that the Betti realization of these classes on Siegel varieties of arbitrary
genus have non-trivial residue on zero dimensional strata of the Baily-Borel
compactification. A direct corollary is the non-vanishing of a higher regulator
map.
