A new approach based on the concept of hopping carrier transport in disordered organic materials is proposed for the description of the electric failure of polymer dielectrics. A steep rise in current during breakdown is associated with structural changes that are induced by a strong electric field and lead to ordering in the mutual arrangement of molecules. As a result, the overlap of the wavefunctions of localized states becomes greater and the mobility of charge carriers increases. The relation of the dielectric strength of polymers to their relaxation properties is elucidated. An increase in the number density and depth of traps enhances the dielectric strength of polymers.