  This paper discusses the elastic behavior of a very long crosslinked
polyelectrolyte chain (Debye-H\"uckel chain), which is weakly charged.
Therefore the response of the crosslinked chain (network) on an external
constant force $f$ acting on the ends of the chain is considered. A
selfconsistent variational computation of an effective field theory is
employed. It is shown, that the modulus of the polyelectrolyte network has two
parts: the first term represents the usual entropy elasticity of connected
flexible chains and the second term takes into account the electrostatic
interaction of the monomers. It is proportional to the squared crosslink
density and the Debye - screening parameter.
