The Apache Point Observatory Galactic Evolution Experiment (APOGEE) is a survey of all Galactic stellar populations that will employ an R=30,000 spectrograph operating in the near-infrared (1.5-1.7μm) wavelength range. The fiber-fed spectrograph is housed in a large (1.4m x 2.3m x 1.3m) stainless steel cryostat or Dewar that is LN2-cooled and will be located in a building near the 2.5m Sloan Digital Sky Survey (SDSS) telescope to which it will be coupled. The choice of shell material and configuration was an optimization among optics packaging, weight, strength, external dimensions, rigging and transportation, the available integration and testing room, and the ultimate instrument room at APO. Internals are fabricated of more traditional 6061-T6 aluminum which is well proven in cryogenic applications. An active thermal shield with MLI blanketing yields an extremely low thermal load of 45-50 watts for this ∼3000 liter instrument. Cryostat design details are discussed with applicable constraints and trade decisions. APOGEE is one of four experiments that are part of Sloan Digital Sky Survey III (SDSS-III).