Abstract: The failure of cement sheath integrity can be easily caused by alternating pressure during large-scale multistage hydraulic fracturing in shale-gas well. An elastic-plastic mechanical model of casing-cement sheath-formation (CSF) system under alternating pressure is established based on the Mohr-Coulomb criterion and thick-walled cylinder theory, and it has been solved by MATLAB programming combining global optimization algorithm with Global Search. The failure mechanism of cement sheath integrity is investigated, by which it can be seen that the formation of interface debonding is mainly related to the plastic strain accumulation, and there is a risk of interface debonding under alternating pressure, once the cement sheath enters plasticity whether in shallow or deep well sections. The matching relationship between the mechanical parameters (elastic modulus and Poisson's ratio) of cement sheath and its integrity failure under alternating pressure in whole well sections is studied, by which it has been found there is a “critical range” in the Poisson's ratio of cement sheath. When the Poisson's ratio is below the “critical range”, there is a positive correlation between the yield internal pressure of cement sheath (SYP) and its elastic modulus. However, when the Poisson's ratio is above the “critical range”, there is a negative correlation. The elastic modulus of cement sheath is closely related to its Poisson's ratio, and restricts each other. Scientific and reasonable matching between mechanical parameters of cement sheath and CSF system under different working conditions can not only reduce the cost, but also protect the cement sheath integrity.