  A lattice model is presented for investigating the fluctuations in static
granular materials under gravitationally induced stress. The model is similar
in spirit to the scalar q-model of Coppersmith et al., but ensures balance of
all components of forces and torques at each site. The geometric randomness in
real granular materials is modeled by choosing random variables at each site,
consistent with the assumption of cohesionless grains. Configurations of the
model can be generated rapidly, allowing the statistical study of relatively
large systems. For a 2D system with rough walls, the model generates
configurations consistent with continuum theories for the average stresses
(unlike the q-model) without requiring the assumption of a constitutive
relation. For a 2D system with periodic boundary conditions, the model
generates single-grain force distributions similar to those obtained from the
q-model with a singular distribution of q's.

Condensed Matter