The state before and after structural failure is quite different, which leads to some sudden changes to its corresponding energy. According to energy catastrophe theory, each phenomenon that reflect system state mutations can regarded as the criterion of instability. Based on the energy catastrophe theory, the problem of concrete structure failure is dealt with various energy calculation methods. Moreover, the energy change rate method is put forward to search the omen point of structure deformation and failure. By comparing with structure total strain energy and plastic strain energy, it is shown that the elastic energy change rate can determine the omen point of structure failure more easily, directly and precisely. Finally, it is found that the stress-strain relationship of many materials in engineering are quite similar, which shows that using elastic energy change rate method to determine the omen point of structure failure has some certain universality in engineering.