  Given a Hamiltonian system on a fiber bundle, there is a Poisson covariant
formulation of the Hamilton equations. When a Lie group G acts freely,
properly, preserving the fibers of the bundle and the Hamiltonian density is
G-invariant, we study the reduction of this formulation to obtain an analogue
of Poisson-Poincar\'e reduction for field theories. This procedure is related
to the Lagrange-Poincar\'e reduction for field theories via a Legendre
transformation. Finally, an application to a model of a charged strand evolving
in an electric field is given.
