Abstract. The general solution of the plane problem in the micropolar-dilatation theory of elasticity is proposed. Such a theory describes a solid in which the fields of displacement, change of the volume (dilatation) and rotation are kinematically independent. The obtained solution is applied to the classical problem of stress concentration around a circular hole in an unbounded micropolar solid with continuously distributed set of voids which is modelled as micropolar-dilatation. An explicit formula for the stress concentration factor is derived which generalizes the earlier results of V. A. Palmov (in the micropolar case) and of S. Cowin (in the dilatation case)