A radio frequency ("RF") shielded and acoustically isolated enclosure that efficiently employs multiple layers of sound insulation and absorbs airborne noise and the noise provided by magnetic resonance imaging ("MRI") equipment through the supports of such equipment. The RF enclosure uses multiple layers and types of insulating materials positioned to maximize the noise absorption of the RF enclosure. This reduces the cost and space required by the enclosure. In one embodiment the enclosure includes a ceiling, a floor and a plurality of walls. The ceiling and walls include one or more multiple layers of different insulating materials that either abut each other or form air gaps. In one embodiment the floor includes a heavy metal plate on which the MRI equipment sits. The plate elastically couples to a conductive shield. The elastic coupling attenuates certain frequencies above the natural frequency of the metal sheet.