Rubber material has a wide range of applications in engineering design because of its unique polymer material properties. Under the action of load, the corresponding relationship between stress and strain is nonlinear, so it is very difficult to make mechanical analysis and material selection in engineering applications. This paper takes butyl rubber as the research object, which obtains stress-strain data through uniaxial compression tests at different strain rates, fits material parameters through MATLAB according to three commonly used hyper-elastic constitutive models, and carries out static finite element simulation analysis based on Ansys. The analysis results are compared with the test results, to verify the practicability and accuracy of the constitutive model and provide a reference for engineering applications.