  We consider the degree 4 L-function associated to an automorphic
representation of the symplectic group GSp(4). Starting with Beilinson's
Eisenstien symbol we construct some motivic cohomology classes on the Shimura
variety of GSp(4). We show that the image of these classes under the absolute
Hodge regulator vanishes on the boundary of the Baily-Borel compactification of
the Shimura variety. This allows to relate these classes to the product of an
archimedean integral, Harris' occcult period invariant, a Deligne period and
the special value of the L-function predicted by Beilinson's conjecture. The
considered representation is assumed to have a Bessel model with respect to an
isotropic symmetric matrix.
