Solution of a contact problem for a rough elastic half-plane is considered. Surface roughness is assumed to be small and stochastic. A perturbation solution of the problem for relatively small roughness with singly connected contact region is proposed and is conveniently expressed in terms of Chebyshev polynomials. Mean distribution of pressure and mean size of the contact are obtained analytically. A pitting model for rough surfaces is considered based on a generalization of an earlier proposed contact model with some stochastic parameters. An analytical formula relating subsurface originated fatigue is considered and fatigue life of rough and smooth surfaces is obtained which shows that fatigue life of rough solids is slightly shorter than of the smooth ones. In the general case of a contact region of rough surfaces with multiple connectivity subsurface originated fatigue possesses properties similar to the case of singly connected contact region. Surface roughness may have a significant effect only on surface and near surface originated fatigue such as wear, micropitting, and shallow flaking.