I used a model proposed by Greenwood and Williamson <1966>, who analyzed closure between a rough surface and a smooth surface under normal stress, to analyze the growth of slip under increasing shear stress, normal stress remaining constant. The two bodies are elastic half-spaces, one rough and one smooth, and Coulomb friction resists slip at sliding contacts. The elastic and dissipative components of the constitutive relation in shear depend upon statistical parameters which describe the topography of the rough surface. I made a parametric study of the effect of topography on the constitutive relations in shear by comparing a model in which the progress of slip at a contact is continuous with one in which the contact goes discontinuously from stuck to sliding. The effect of topography was also studied by assuming that the probability density distribution of the heights of asperities is Gaussian or, alternatively, a negative exponential. These variations in topography produced only minor differences in the constitutive behavior. This insensitivity of the constitutive behavior to differences in the statistical description of the topography arises in part because, only relatively, a small range of asperity heights is active in typical experiments. Work done against friction introduces a dissipative component into the constitutive behavior which I evaluated analytically; I show that the components have a simple graphical construction on plots of shear stress versus displacement developed from experimental observations. Sliding in the reverse sense which occurs when the applied shear stress is relaxed is analyzed, resulting in expressions which describe the shape of hysteresis loops formed when shear stress is cycled. Introducing measurements made on surfaces of specimens of granite and quartzite into the theoretical relations, I found reasonable agreement with experimental data.