A dynamic double torsion testing machine and measurement system were developed on the basis of the split Hopkinson pressure bar test and the theoretical one-dimensional wave propagation in the input and output bars, and their validity was confirmed by measuring the dynamic fracture toughnesses of non-stoichiometrically cured epoxy resins. The applicable range of the stress intensity factor, as formulated by Fuller was determined from the specimen shape and loading conditions for the dynamic double torsion test. The available crack length was found to be below 70% of the specimen length by measuring the static fracture toughness and analyzing the natural frequency of the specimen. The duration of the impact force until dynamic fracture in the dynamic double torsion test was found to be longer than the reciprocal of the lowest natural frequency of the out-of-plane bending mode of the specimen, as expressed by an approximate equation. Because the mechanical properties of the epoxy resin had little dependency on time in the experiments at room temperature, the validity of the testing machine and measuring system were able to be confirmed by comparing the dynamic and static fracture toughnesses of the epoxy resins and observing the fracture surfaces.