An illustrative example embodiment of an elevator sheave assembly (30) includes a plurality of polymer rings (40, 50) that are secured together. The plurality of polymer rings (40,50) includes at least two polymer rings (40, 50) that each have an outer circumferential surface (42, 52) that defines a portion of a belt guiding surface (44, 54) adjacent a flange (46, 56) at a longitudinal end of the sheave assembly (30). The at least two polymer rings (40, 50) each include a bearing (70) supported inside the ring (40, 50).