We study a scalar lattice model for intergrain forces in static, noncohesive, granular materials, obtaining two primary results: (i) The applied stress as a function of overall strain shows a power law dependence with a nontrivial exponent, which moreover varies with system geometry; and (ii) probability distributions for forces on individual grains appear Gaussian at all stages of compression, showing no evidence of exponential tails. With regard to both results, we identify correlations responsible for deviations from previously suggested theories.