The method for quantitative analysis of the kinetics of damage accumulation in the structure of series of polymer samples at stretching is proposed. The proposed approach is to calculate the fractality indices of time series by means of a minimum coverage method, followed by a failure frequency analysis, while increasing the levels of applied stresses and relative deformations. Epoxy polymer based on ED-20 resin hardened by Etal-1460 hardener, was selected as the object of the study. The results of the study of changes in elastic-strength indicators and levels of “critical” stresses and relative elongation in the stretching of epoxy polymer during the natural climate impact are presented.