Research results of influence of afterglow of low temperature oxygen plasma onto surface of a polyethylene and also of some materials on a poly (ethylene terephthalate) basis are resulted. The simplified variant of a technique resulting in the kinetic characteristics of interaction of atoms О(3Р) with polymers (rate coefficients and probabilities of heterogeneous decay of atoms) is offered. In basis of this technique lies the equation of continuity for a stream of oxygen atoms and assumption about defining role of atomic oxygen in weight loss of polymer. Wide intervals of gas pressure, discharge current and temperature sample are used. Results show that the oxidative destruction process in activated oxygen in afterglow is multi-channel and multistage that and its kinetic characteristics are effective.