This chapter describes Eshelby’s technique for determining the stress and strain in regions in an infinite elastic body that undergo a change of size or shape. The technique is also extended to determine the stress and strain in regions of different elastic properties than the surroundings due to loading in the farfield. The chapter also discusses the relation of this technique to singular solutions in elasticity and different integral forms for the solutions. Example applications of the technique include determining the effective stress in a narrow fault zone, the stress and strain in a fluid reservoir and subsidence due to fluid mass injection or withdrawal. The approach of Eshelby is also used as a basis for a brief description of representations of deformation due to slip and seismic source theory.