Based on traditional manufacturing concept, the significance of phase structure\|condensed state about PMMA deforming in Tg～Tf  temperature range are discussed. To this polymer, low and high temperature zones for high\|elastic(rubber\|like) deforming were plot out  between Tg and Tf  using golden section, and meantime their experimental temperatures under high-elastic(rubber\|like) state were designed for hot compression. As upsetting deformation and specimen in cold compression study recently published, hot compression experiments for high\|elastic state PMMA are done by using four kinds of deformation rate and three kinds of deformation degree. In the experiments, PMMA would be behaved with soft and tough property during low temperature deforming under its high elastic state, and would have tendency of viscous flow deforming during high temperature deforming under its high elastic state. The limit deformation degree would be increased; the maximum and average ratios of strain recovery were respectively 5.9% and 2.3% after load removal.Therefore, the shape fixbility can be controlled during hot forged PMMA under high\|elastic state and this technique will be usable in manufacturing.