The research background is the elastic ring squeeze film damper. Four contact pressure models were established by analyzing the structural characteristics and movement, combined with the sliding bearing theory, including structural parameters and eccentricities. Multi-structure and multi-interval dynamic boundary conditions were selected by analyzing actual structures. Simpson, polynomial, and integrated parameters methods extended Booker formulas. By combining existences and forms of the solution and mean-value theories, approximate analytical solutions of the finite length bearing were obtained under different contacts. Combined with the short and long bearing, general structures and expressions of analytical solutions of oil film pressures and forces under three approximation theories were obtained. The oil film characteristics of the dynamic equilibrium state were obtained, and the correctness was verified by theoretical comparison. Numerical simulations analyzed the relationship among relevant parameters. It provided a theoretical basis upon which to study the geometric form, motion state, and the approximate analytical solution of the ERSFD dynamic model, and increased its research ability.