To address the shortcomings of poor isolation performance in traditional rubber vertical seismic isolation devices and the large deformation in spring vertical seismic isolation devices, an air spring vertical seismic isolation device (ASVSID) utilizing compressed air for seismic isolation was proposed. The construction of the ASVSID was introduced, the material properties of the air spring (AS) capsule skin based on single and biaxial stress state were tested, the vertical mechanical properties of the ASVSID were experimentally studied, and the finite element (FE) method and the calculation method of the ASVSID based on biaxial stress state of the AS capsule skin were given. The research results show that the load displacement of the ASVSID exhibits nonlinear characteristics, and its vertical mechanical properties are obviously affected by air pressure of the AS. The material properties of the AS capsule skin are different under single and biaxial stress state. Through comparison with the test results, the proposed FE method based on biaxial stress state of the AS capsule skin can accurately simulate the ASVSID. In addition, the calculation method based on biaxial stress state of the AS capsule skin also can accurately calculate the vertical mechanical property parameters of the ASVSID.