Abstract: A slip over, sound muffling cover for a machine such as a compressor is disclosed which includes an outer layer of relatively rigid, bendable, resilient material capable of being distorted and returned to its desired shape, and an inner layer of flexible, sound absorbent material. The outer layer includes a cap having a broad surface and a pair of open sided trays attached on corresponding ends thereof to the broad surface so that, under normal circumstances, the open sides of the trays face one another. Each of the trays contains a pair of elongated flanges on opposite side edges thereof, pairs of such flanges which oppose one another on the same side of the trays are closable against one another to enclose a machine in the sound absorbent material.