For the cloud computing system, combined with the memory function and incomplete matching of the biological immune system, a formal modeling and analysis method of the cloud computing system survivability is proposed by analyzing the survival situation of critical cloud services. First, on the basis of the SAIR(susceptible, active, infected, recovered) model, the SEIRS(susceptible, exposed, infected, recovered, susceptible) model and the vulnerability diffusion model of the distributed virtual system, the evolution state of the virus is divided into six types, and then the diffusion rules of the virus in the service domain of the cloud computing system and the propagation rules between service domains are analyzed. Finally, on the basis of Bio-PEPA(biological-performance evaluation process algebra), the formalized modeling of the survivability evolution of critical cloud services is made, and the SLIRAS ( susceptible, latent, infected, recovered, antidotal, susceptible) model is obtained. Based on the stochastic simulation and the ODEs (ordinary differential equations) simulation of the Bio-PEPA model, the sensitivity parameters of the model are analyzed from three aspects, namely, the virus propagation speed of inter-domain, recovery ability and memory ability. The results show that the proposed model has high approximate fitting degree to the actual cloud computing system, and it can well reflect the survivable change of the system.