In order to study the landing stability of the leg buffer platform, combined with the characteristics of the clay damper, a dynamic model of the legged-type buffer platform was established. Based on the theory of zero moment point (ZMP) to determine the dynamic stability, the ZMP coordinate formula of the legged-type buffer platform is obtained. And the stability criteria of the ZMP-quadrilateral rule and ZMP offset rule are proposed. The results show that criterion can determine the landing stability of the platform and obtain the parameters response rules that affect the stability of the platform, and provide reference for the further optimization design of the legged-type buffer platform.