Abstract. The problem of determining the stress and couple-stress fields within a single micropolar inhomogeneity, immersed into an unbounded micropolar matrix loaded at infinity, is discussed. Using Eshelby's method, an approximate solution of the problem is found for the case of spherical inhomogeneity. In order to analyse the applicability of this solution, a system of integral equations is delivered which describes the strain fields in the micropolar body with a micropolar inhomogeneity in it, and an iterative process, solving the system, is proposed. The first step of this process leads to the approximate solution, found by Eshelby's method. It is shown, too, that the approximate solution is the linear part of the asymptotic expansion in the case of vanishing difference between the micropolar moduli of the matrix and the inhomogeneity.