A machine and a method for forming a rim of a paperboard container having a bottom and a sidewall terminating at a rim are disclosed. The machine includes a frame, a turret rotatably coupled to the frame, a plurality of circumferentially spaced pockets supported by the turret and a plurality of workstations about the turret. Each pocket includes a shell having a cavity with a mouth configured to receive the container along an axis and a first member about the cavity and including a first surface. The first surface is one of a flat surface and a concave surface and is actuatable along the axis from a retracted position below the mouth to an extended position adjacent the mouth. The plurality of workstations includes a first station and a second station. The first station has a first tool with a second surface, wherein the second surface is said one of a flat surface and a concave surface. The first tool is adapted to move along the axis so as to engage and form the paperboard rim between the first and second surfaces. The second station includes a second tool having a third surface, wherein the third surface is the other of a flat surface and a concave surface. The second station further includes a plurality of die segments about the second tool. Each segment has a fourth surface, wherein the fourth surface is the other of a flat surface and a concave surface. The die segments are adapted to move along the axis and to pivot between a closed position in which the fourth surface engages and forms a rim and an opened position.