Sheet-shaped poly(ether-ether-ketone) (PEEK), silicone rubber (SiR), flame-retardant (FR) ethylene-propylene-diene monomer rubber (EPDM), and FR crosslinked polyethylene (FR-XLPE) were aged thermally at various temperatures with or without concurrent irradiation of gamma rays. The degradation mechanism was examined extensively by instrumental analyses, while those in mechanical and dielectric properties were evaluated by measuring indenter modulus, elongation at break, tensile strength, electrical conductivity, and complex permittivity. The behavior and its underlying mechanism of degradation induced by heat and radiation are quite different among these polymeric insulating materials. All the four materials exhibit deterioration in mechanical properties at a much earlier stage of aging than that in dielectric properties. Therefore, mechanical parameters are important indicators that should be considered in the condition monitoring.