Abstract: Under the service environment, the structure of metal materials often undergoes a complex process from the micro-damage to the macro-failure. In order to better understand the degeneration mechanism, the CAS wavelet is used to solve the differential equation of the fatigue crack propagation, and the differential equation is transformed into algebraic equations. Then the reliability of a cracked structure in a general environment and a corrosion environment is analyzed with the algebraic equations. At last, by comparing the calculated results with the experiment results, it is shown that the CAS wavelet method can realize a smooth transition from the short crack to the long crack.