Statistical theories of rough elastic contact have previously been developed for the contact of spheres and of parallel cylinders, and have predicted stress distributions significantly different from those of the classical Hertzian theory. The theories characterize the surface in terms of three surface parameters describing, respectively, the roughness, density and radius of curvature of the asperities. In this paper, a procedure is described for quantifying these theories by obtaining the surface parameters from the spectral-moment approach to surface description; the only surface measurement needed is one of roughness. The procedure is illustrated by two numerical examples relating to the contact of a rocker arm with a pushrod and to a journal bearing. In the case of the rocker and pushrod, no significant difference from the smooth-surface results is found. In the case of the journal bearing, however, the maximum stress is calculated to be 36 percent less, and the nominal contact width 2.2 times more, than the respective figures for smooth contact.