Four kinds of polymer matrix composites (filler, E-glass or carbon fibre cloth; matrix, epoxy or polyimide resin) and pure epoxy and polyimide resins were irradiated with 60Co γ-rays or 2 MeV electrons at room temperature. Mechanical tests were then carried out at 77 K and at room temperature. Following irradiation, the Young's (tensile) modulus of these composites and pure resins remains practically unchanged even at 170 MGy for both test temperatures. The ultimate strength, however, decreases appreciably with increasing dose. The dose dependence of the composite strength depends not only on the combination of fibre and matrix in the composite but also on the test temperature. A relationship is found between the composite ultimate strain and the matrix ultimate strain, thus indicating that the dose dependence of the composite strength is virtually determined by a change in the matrix ultimate strain due to irradiation. Based on this finding, we propose a mechanism of radiation-induced degradation of a polymer matrix composite in order to explain the dose dependence of the composite strength measured at 77 K and at room temperature.