A steady plane flow of incompressible fluid around a bluff body at high Reynolds number (Re) is investigated by the method of matched asymptotic expansions. It is determined on the assumption of a nonzero drag coefficient at Re → ∞ that the separated region as a whole in the general approximation is an ellipse of a small relative thickness. Its longitudinal and transverse sizes grow proportionally to Re and Re1/2, respectively. On a body scale, the Kirchhoff model of flow with free streamlines takes place.