Interface interactions play a pivotal role in the mechanics of particulate and fractured materials. A mechanistic approach is adopted to model the force-deformation behavior of rough interfaces which are considered to interact via asperity contacts. Elastic deformation as well as frictional sliding are considered at asperity contacts. The topography of the interface is represented by means of statistical distributions of asperity contact orientations, asperity heights, and asperity curvature. The resulting model is used to predict the normal stiffness and the shear stiffness of the interface.