The two way couple model of elastic ring squeeze film damper(ERSFD) was established through numerical approach. The governing equation of the fluid block was obtained by Reynolds equation and the equation of motion of the elastic ring was solved by finite element method with thick plate. The coupled equations were solved through block iteration method. The transient pressure profile of inner film and outer film were obtained and the force coefficients of ERSFD were identified. The results show that the height of the boss has significant influence on the damping of the ERSFD. The increase of the height of the boss from 0.15mm to 0.30mm results in a drop of damping from 5790(N·s)/m to 718(N·s)/m. The stiffness coefficients of ERSFD have close relations with the thickness of the ring as well as the number of boss. The increase of thickness of elastic ring from 0.8mm to 1.0mm leads to the increase of the stiffness coefficients from 1.44×106N/m to 2.51×106N/m.