Heat treating UHMWPE by applying pressure with radial constraint at suitable times during a heating protocol reduces or eliminates cavitation, which is otherwise observed to occur when the UHMWPE is heated to a temperature above 300° C. Heat treated UHMWPE can undergo subsequent processing involving crosslinking, deformation, doping with antioxidant, and homogenizing or annealing. Heating during these steps can be carried out even above the onset melt temperature of the UHMWPE without loss of physical properties.