  Stress patterns in static granular media exhibit unusual features when
compared to either liquids or elastic solids. Qualitatively, we attribute these
features to the presence of `stress paths', whose geometry depends on the
construction history and controls the propagation of stresses. Stress paths can
cause random focussing of stresses (large fluctuations) as well as systematic
deflections (arching). We describe simple physical models that capture some of
these effects. In these models, the `stress paths' become identified with the
characteristic `light rays' of wavelike (hyperbolic) equations for force
propagation. Such models account for the `pressure dip' below conical sandpiles
built by pouring from a point source, and explain qualitatively the large
stress fluctuations observed experimentally in granular matter. The differences
between this approach and more conventional modelling strategies (based on
elastoplastic or rigid-plastic models) are highlighted, focusing on the role of
boundary conditions. Our models provide a continuum picture in which granular
materials are viewed as fragile matter, able to support without rearranging
only a subset of the static external loadings admissible for a normal elastic
solid.
