The category of problems which examines the mechanical behaviour of contact regions constitutes an important branch of applied mechanics with extensive engineering applications. The results of such research can be applied to the study of mechanics of composite materials, tribology, soil-foundation interaction, mechanics of rock interfaces, modelling of damage phenomena and micro-mechanics. In classical studies, the modelling of interface responses has focussed on purely idealized forms of interface phenomena which range from frictionless contact to bonded contact, with Coulomb friction or finite friction occupying an intermediate position. Current research has attempted to improve such modelling by endowing the interface with its own characteristic constitutive responses. This research indicates the significant manner in which non linear, frictional, dilatant, hardening and softening interface constitutive responses can influence the global and local interface responses of engineering interest.The technical sessions held in New Mexico (sponsored by the Elasticity Committee of the Engineering Mechanics Division of the American Society of Civil Engineers) brought together new advances in the theoretical formulation, analysis and the application of material interface modelling to problems of engineering interest. This book contains the papers presented plus invited contributions from leading researchers.