This paper describes modelling and analysis of bump floating ring seal with the bump effect and the fluid dynamic effect of floating ring seal. A numerical analysis method is developed and implemented for predicting the BFRSs' lock-up eccentricity ratio, leakage flow-rate, rotordynamic force coefficients and attitude-angle. Also, the comparison of the BFRSs' properties with those of the conventional FRSs, having common geometric parameters and operating conditions, is performed. A turbulent bulk-flow model is used to predict the flow and rotordynamic parameters. From the analytical results, the lock-up eccentricity reduces by 50% FRSs, the BFRSs' direct stiffness and damping coefficients are higher, and cross-coupled terms are less responsive to changing rotor-speed. Although, the lock-up eccentricity is smaller, the sealing effectiveness remains unchanged. The predictions are reasonably in good agreement with test data, except the attitude-angles are over-predicted.