The paper by John Douglas Eshelby, titled "The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems," published in the Proceedings of the Royal Society of London, Series A, in 1957, addresses the determination of the elastic field around an ellipsoidal inclusion in an isotropic elastic solid. The author proposes a method using a sequence of imaginary cutting, straining, and welding operations to simplify the problem. For an ellipsoid, the strain inside is uniform and can be expressed using elliptic integrals. This method is then extended to solve the problem of how an applied stress field is disturbed by an ellipsoidal inhomogeneity. The paper provides explicit solutions for various physical and engineering problems, including the elastic field far from an inclusion, stress and strain components at the boundary, total strain energy, interaction energy, and changes in elastic constants due to the presence of inhomogeneities. The results are applicable to both arbitrary inclusions and ellipsoids, with detailed calculations for specific cases such as spheres and ellipsoids with different elastic constants. The paper also discusses the effective elastic properties of materials containing a uniform dispersion of ellipsoidal inhomogeneities.The paper by John Douglas Eshelby, titled "The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems," published in the Proceedings of the Royal Society of London, Series A, in 1957, addresses the determination of the elastic field around an ellipsoidal inclusion in an isotropic elastic solid. The author proposes a method using a sequence of imaginary cutting, straining, and welding operations to simplify the problem. For an ellipsoid, the strain inside is uniform and can be expressed using elliptic integrals. This method is then extended to solve the problem of how an applied stress field is disturbed by an ellipsoidal inhomogeneity. The paper provides explicit solutions for various physical and engineering problems, including the elastic field far from an inclusion, stress and strain components at the boundary, total strain energy, interaction energy, and changes in elastic constants due to the presence of inhomogeneities. The results are applicable to both arbitrary inclusions and ellipsoids, with detailed calculations for specific cases such as spheres and ellipsoids with different elastic constants. The paper also discusses the effective elastic properties of materials containing a uniform dispersion of ellipsoidal inhomogeneities.