A small volume and high stiffness periodic metal isolator composed of elastic plates and supporting columns is designed. Firstly, the static load test is carried out by using microcomputer controlled electronic testing machine, and the load-displacement characteristic curve is obtained. Based on the finite element method, a finite element model of periodic structure is established, and the static analysis is carried out under the same working conditions as the test. On this basis, the influence of the main dimension parameters on the stiffness is studied. The results show that the thickness of elastic sheet has great influence on the stiffness, while the inner diameter and the number of layers have little influence on the stiffness. Finally, by using the equivalent spring-mass model of the periodic structure isolator with multiple degrees of freedom, its dynamic equation is established by means of modal superposition method, and the expression of force transfer rate is deduced. A simulation is carried out based on the finite element analysis which is verified by experiment. The results show that the theory and simulation match well. When the load mass exceeds a certain value, the periodic structure can be simplified to single degree of freedom.