Sliding of a rough surface having a range of asperity heights is a gradual process, starting at contacts under relatively low normal shear load and spreading until the surface slides as a unit. We analyze this process theoretically for asperities with spherical tips, with heights having a probability density distribution given by a negative exponential. The case where applied normal traction increases concurrently with applied shear is treated in detail, resulting in analytical expressions for the normal and shear displacements. These results are used to show limitations on constitutive behavior for more complex normal stress-shear stress histories.