Quantitative description of the effect of gamma -irradiation of PE and PMMA on positronium formation on the trapped electrons at low temperatures is suggested. The consideration shows that, at least in these substances, the number of the trapping centers is always enough to localize all ortho-positronium, and therefore the intensity of the long-lived positronium component is dependent only on the probability of Ps formation but not on the number of the trapping centers.