  We investigate in detail two models describing how stresses propagate and
fluctuate in granular media. The first one is a scalar model where only the
vertical component of the stress tensor is considered. In the continuum limit,
this model is equivalent to a diffusion equation (where the r\^ole of time is
played by the vertical coordinate) plus a randomly varying convection term. We
calculate the response and correlation function of this model, and discuss
several properties, in particular related to the stress distribution function.
We then turn to the tensorial model, where the basic starting point is a wave
equation which, in the absence of disorder, leads to a ray-like propagation of
stress. In the presence of disorder, the rays acquire a diffusive width and the
angle of propagation is shifted. A striking feature is that the response
function becomes negative, which suggests that the contact network is
mechanically unstable to very weak perturbations. The stress correlation
function reveals characteristic features related to the ray-like propagation,
which are absent in the scalar description. Our analytical calculations are
confirmed and extended by a numerical analysis of the stochastic wave equation.
