The floating ring seal has the ability of minimizing clearance without rubbing phenomenon. However, the seal ring can be unstable due to extremely high lock-up eccentricity ratio arisen from the poor design of height and surface finish of the ring. The exact prediction of the lock-up position of the floating ring is necessary to design the floating ring properly. The governing equations are developed and solved numerically. The test facility for the measurement of the boundary-lubrication-friction coefficient of the ring‘s surface has been established. Based on the results of analysis, the geometric conditions of the floating ring seal are suggested for operating at a low lock-up eccentricity ratio.