Complex variable techniques and the pseudo-stress function are used to obtain the stress distribution in power-law materials containing a single rigid inclusion subjected to either a uniaxial tensile stress or a simple shear stress. It is argued that certain discrepancies with a former investigator’s results, especially in a neighborhood of the inclusion surface, are to be attributed to a different treatment of stress singularities. The influence of the strain-rate hardening exponent on the stress field (in particular, on the stress concentration factor) is also considered.