This paper presents a study of the steady plane shear flow of a dense assembly of frictional, inelastic disks using discrete simulation. The pressure and shear rate are prescribed, and the shear state is determined by a single dimensionless number, the inertial number I, which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasi-static regime of soil mechanics, while large values correspond to the collisional regime of kinetic theory. The shear states are homogeneous and become intermittent in the quasi-static regime. In the intermediate regime, the solid fraction decreases linearly from the maximum packing value, and the effective friction coefficient increases linearly from the static internal friction value. From these dilatancy and friction laws, the constitutive law for dense granular flows is deduced, with a plastic Coulomb term and a viscous Bagnold term. The relative velocity fluctuations follow a scaling law as a function of I. The mechanical characteristics of the grains have a very small influence in this intermediate regime. The friction law is related to the angular distribution of contact forces, and the local frictional forces have a small contribution to the macroscopic friction. The paper also describes the shear localization when gravity is added. The results are presented in terms of an effective friction coefficient μ* = S/P, which should come close to tanφ in the limit of slow motion. The study shows that the inertial number I is a fundamental quantity to describe the rheology of granular materials, as it characterizes the flow regime and allows for the progressive transition between the quasi-static and dynamical regimes. The paper also discusses the influence of the mechanical properties of the grains on the dilatancy and friction laws.This paper presents a study of the steady plane shear flow of a dense assembly of frictional, inelastic disks using discrete simulation. The pressure and shear rate are prescribed, and the shear state is determined by a single dimensionless number, the inertial number I, which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasi-static regime of soil mechanics, while large values correspond to the collisional regime of kinetic theory. The shear states are homogeneous and become intermittent in the quasi-static regime. In the intermediate regime, the solid fraction decreases linearly from the maximum packing value, and the effective friction coefficient increases linearly from the static internal friction value. From these dilatancy and friction laws, the constitutive law for dense granular flows is deduced, with a plastic Coulomb term and a viscous Bagnold term. The relative velocity fluctuations follow a scaling law as a function of I. The mechanical characteristics of the grains have a very small influence in this intermediate regime. The friction law is related to the angular distribution of contact forces, and the local frictional forces have a small contribution to the macroscopic friction. The paper also describes the shear localization when gravity is added. The results are presented in terms of an effective friction coefficient μ* = S/P, which should come close to tanφ in the limit of slow motion. The study shows that the inertial number I is a fundamental quantity to describe the rheology of granular materials, as it characterizes the flow regime and allows for the progressive transition between the quasi-static and dynamical regimes. The paper also discusses the influence of the mechanical properties of the grains on the dilatancy and friction laws.