It was the last book the outstanding mathematician, mechanician and lecturer S. G. Mikhlin took an active part in writing. Having been completed during his lifetime, this book could not be published in Russia due to well- know difficulties. Since that time new results in integral equations of elasticity theory have appeared. The works of W. Wendland and his school on numerical methods of solving boundary integral equations, the works of I. Chudinovich on inves- tigation of non-stationary integral equations, the works of S. Kuznetsov con- nected with the construction of the fundamental solutions for anisotropic me- dia and others deserve special mentioning. The authors recognize that though the book is devoted to integral equations of elasticity theory, its contents do not cover all possible directions in this field. So the book does not contain the investigations of pseudo-differential equations of three-dimensional prob- lems of elasticity theory, connected with the works of R. Goldstein, I. Klein, G. Eskin; the questions of solving by integral transformations (I. Ufland, L. Slepian, B. Buda. e: v); the theory of symbols of pseudo-differential operators on non-smooth surfaces developed in the works of B. Plamenevski et al. and the new methods of numerical solution of pseudo-differential equations as developed by a school of V. Mazya. The present book gives the classical methods of potential theory in elas- ticity and their development and also the solution of a number of problems which here are published in English for the first time.