Thin inclusions which elastic moduli differ substantially from the moduli of the host medium are considered. Such inclusions are characterized by two dimensionless small parameters: the ratio of the characteristic linear sizes of the inclusion and the ratio of the characteristic elastic moduli of the inclusion and the host medium. The principal terms of the asymptotic expansions of the elastic fields in the medium with thin inclusions with respect to these parameters are derived. The elasticity problems for thin soft and thin stiff inclusions are reduced to 2D integral equations on the inclusion middle surfaces. For thin ellipsoidal inclusions, explicit analytical solutions of these equations are presented.