The present study analyzes the known expressions establishing exponential and power relationships between the lifetime of polymer dielectrics and the strength of the electric field acting on them. The work notes the necessity of mathematical substantiation of the known power expression for the field dependence of electrical lifetime. We obtained the equation of dependence of the electrical lifetime of polymeric dielectrics on the value of the applied electric field strength within the framework of the mathematical catastrophe theory. The study has the performance of quantitative estimation of the parameters of this equation for paper, epoxy and polyethylene terephthalate electrical insulation. We established a good agreement between the literature experimental data and the field dependences of the electrical lifetime of polymers plotted by the proposed equation. The study analyses geometric images of the fold catastrophe function reflecting the nature of the change in the dimensionless parameter of the rate of damage accumulation in a polyethylene terephthalate film under varying electric field strength. The paper shows the prospect of using the mathematical apparatus of catastrophe theory to describe experimental regularities of changes in the electrical strength properties of polymer dielectrics in strong electric fields.