This book deals with contact mechanics of piezo – electro – magneto – elastic materials. An analytical formulae which describe full coupled fields in “smart” material under general external loadings, different shapes of punches and some class of boundary conditions are solved and analyzed. Unlike in the case of elastic materials, contact problems in magneto – electro – elastic materials (MEEMs) involve some fundamental issues that are not yet resolved. The methodology presented in this book is recapitulated from author’s papers to make contact problems for MEEMs self – sufficient for a reader. My book clarified some questions encountered in contact mechanics of “smart” composite materials made by MEEMs. Nowadays, MEEMs and composites made from them have wide range in engineering applications such as space planes, supersonic, air plane rockets, missiles fusion, reactors and submarines.