This thoroughly revised and updated edition of the classic text on surface mechanics preserves the objectives of the original: the rigorous derivation of surface properties such as temperature and deformation from the differential equations of continuum mechanics. From such solutions for the surfaces of single bodies one can then formulate problems involving two bodies at rest or in relative motion in terms of a singular integral equation. The discussion is analytical and theoretical, but animated by the authors’ decades of experience in applications and experimental mechanics. This new edition has been updated to include many technologically motivated problems and solutions, especially computer solutions. Beginning with a survey of the field equations of classical continuum mechanics, the book continues with a discussion of surface temperatures in moving bodies. It then turns to semi-infinite and layered elastic media, discussing stress and deformation as well as thermal stress and associate deformation fields. Treatments of viscoelasticity and perfect plasticity concentrate on semi-infinite solids; these are followed by a discussion of rough surfaces. The book concludes with a lengthy chapter of applications. An appendix discusses integral equations. Intended for graduate students of mechanics and mechanical engineering, the book will also be of interest to applied mathematicians and others interested in tribology.