The paper describes computer simulation of granular materials under dense conditions when particles are in persistent contact with their neighbors. Two regimes are observed in this limit, one for which the stresses scale with both elastic and inertial properties, and a non-inertial quasi-static regime in which the stresses scale are purely elastic. In these elastic regimes, the forces are generated by internal force chains. Reducing the concentration slightly causes a transition from an elastic to a purely inertial behavior. This transition occurs so abruptly that a \(2\%\) concentration reduction can be accompanied by nearly three orders of magnitude of stress reduction. This indicates that the granular flows near this limit are prone to instabilities. Unexpectedly, there is no path between inertial flow and quasi-static flow. Finally, the author investigates the effects of nonlinear contacts, and proposes an appropriate scaling that accounts for the nonlinear behavior in elastic quasi-static regime.