Abstract : The plastic flow of granular materials reflects to a large extent the constraints imposed by steric exclusions and mechanical equilibrium at the particle scale. An accurate formulation of these local constraints is the key to a statistical mechanical approach but requires a rich set of state parameters. We show that the constraints can be taken into account in a simple way with a reduced set of anisotropy parameters akin to the lowest-order description of the contact and force networks. We then introduce a model of kinematic jamming defined as a state of saturation in the evolution of the contact network. This model correctly predicts the accessible geometrical states as well as the evolution of the system to a kinematically jammed state. We also show that a harmonic decomposition of shear stress as a function of the anisotropy parameters and phase factors representing the loading history leads to the "fragile" character of force networks.