Abstract A uniform elastic medium with an inclusion in the shape of an elongated solid of revolution is considered. It is assumed that the elastic moduli of the medium are much small than the elastic moduli of the inclusion (stiff rod). The principal term is constructed for the expansion of the elastic fields in a medium with a stiff rod in a series of small parameters of the problem: the ratio between the characteristic linear dimensions of the inclusion and the ratio between the elastic moduli of the medium and the inclusion. The part of the principal term of the “inner” expansion, the stress field within the rod, that varies slowly along the rod axis, is determined by a method described in /1/. Rods with a different change in the radius of the transverse section along the axis, in the shape of a cylinder, an elongated ellipsoid, and a tapered spindle are considered. By using a well-known integral operator the principal term of the desired expansion of the elastic fields outside the rods is restored according to the known inner expansion.