The vibrational relaxation of oxygen embedded in an argon cage through vibrational to local translation, rotation, and argon phonon modes has been studied using semiclassical procedures. The collision model is based on the trapped molecule undergoing the restricted motions (local translation and hindered rotation) in a cage formed by its twelve nearest argon neighbors in a face-centered-cubic structure. At 85 K in the liquid argon temperature range, the deexcitation probability of O-2(v=1) is 5.8x10(-12) and the relaxation rate constant with the collision frequency from local translation is 23 s(-1). The rate constant decreases to 5.1 s(-1) at 50 K and to 0.016 s(-1) at 10 K in the solid argon temperature range. Transfer of the vibrational energy to local translation, rotation (both hindered and free), and argon phonon modes is the relaxation pathway for the trapped oxygen molecule. (C) 2004 American Institute of Physics.