An example elevator machine frame assembly (30) includes a plurality of support plates (32) configured to support at least selected portions of. an elevator machine including a traction sheave (24). The support plates each comprise a plurality of mounting surfaces (50) that are aligned within a plane that intersects with an axis of rotation (56) of a traction sheave that is supported by the frame assembly. A plurality of support rods (36) are connected to the support plates (32). The support rods maintain a desired spacing between the plates and a desired alignment of the plates relative to each other. In a disclosed example, the support rods include a sound dampening material (44) such as sand in an interior of the rods.