Because the solutions based on the numerical integration of the complete Navier-Stokes equations can be very time-consuming, the bulk-flow model was used for calculating the static and the dynamic characteristics of floating ring seals. The bulk-flow model is governed by three partial differential equations on eccentric working conditions with steepest descent method to find the seal's equilibrium position efficiently. A finite difference scheme has been used to solve the nonlinear governing equations. Compared to Nelson and Nguyen's Fast Fourier Transform Method, this scheme has better consistency. Perturbation analysis of the flow variables yields a set of zeroth and first-order equations. The SIMPLE algorithm is used to integrate the system of bulk-flow equations. Comparisons of the numerical predictions (lock-up eccentricity ratio, leakage flow rate and rotordynamic coefficients) with Ha's results, which were formulated using the Fourier series, and experimental data are presented subsequently.