The glass transition pressurePgfor a polyurethane elastomer (Solithane 113, 50/50 resin‐catalist ratio, manufactured by Thiokol Chemical Co.) is located at 2.5 kbar at room temperature and the glass transition temperatureTgis at −20 °C. Mechanical behavior of the elastomer, namely the tensile and the compressive stress‐strain behavior, in the glassy state as well as in the rubbery state has been determined. The Young’s modulus increases from ∼107dyn/cm2in the rubbery state to ∼1010dyn/cm2in the glassy state. The tensile fracture strain increases rapidly from 60% at atmospheric pressure to greater than ∼200% at 1 kbar and higher. In the glassy state, the samples exhibit yielding, yield drop, and cold drawing. The yield drop is not accompanied by necking. Rather the samples undergo uniform drawing throughout the entire gage length. A series of sequential loading, unloading, and reloading tests in the plastic range was also conducted in the glassy state. It was observed that the plastic strain recovers as a function of time, that the yield maximum reappeared and grew after a delay time, and that the Young’s modulus in subsequent loadings was higher than the initial values and increased steadily with time. Various loading histories can be completely erased upon returning to a rubbery state by removal of applied pressure. The recovery of the plastic deformation, or the viscoplastic behavior, occurs at essentially the same rate at all pressures tested, and thus the data were superimposable to form a master curve nearPg. A molecular explanation for the various new phenomena observed is given.