  A {\it stochastic adhesion} model is introduced, with the purpose of
describing the formation and evolution of mildly nonlinear structures, such as
sheets and filaments, in the intergalactic medium (IGM), after hydrogen
reionization. The model is based on replacing the overall force acting on the
baryon fluid -- as it results from the composition of local gravity, pressure
gradients and Hubble drag -- by a mock external force, self-consistently
calculated from first-order perturbation theory. A small kinematic viscosity
term prevents shell-crossing on small scales (which arises because of the
approximate treatment of pressure gradients). The emerging scheme is an
extension of the well-known adhesion approximation for the dark matter
dynamics, from which it only differs by the presence of a small-scale `random'
force, characterizing the IGM. Our algorithm is the ideal tool to obtain the
skeleton of the IGM distribution, which is responsible for the structure
observed in the low-column density Ly$\alpha$ forest in the absorption spectra
of distant quasars.
