Positron annihilation lifetime spectroscopy (PALS) has widely been used for probing open volume defects in various materials. PALS is in principle non-destructive, yet conventional PALS is not strictly non-destructive because cutting out of two specimens from the material is required. Recently we developed a novel method of PALS, which is potentially applicable to nondestructive, onsite material inspection. In order to explore the possibility of onsite monitoring of polymer degradation by this novel method of PALS, we studied variations of positron lifetime and mechanical properties of ultra high molecular weight polyethylene (UHMWPE) subjected to γ-irradiation. Correlations were found between the mechanical properties and ortho-positronium lifetimes, suggesting the feasibility of non-destructive, onsite monitoring of polymer degradation by PALS. The effect of γ-irradiation on positronium formation is discussed.