Static and dynamic characteristics of labyrinth seals are important in the prediction of the stability of turbomachinery. The paper presents an effective numerical method to predict the static and dynamic performance characteristics of seals at off-center conditions with different rotor whirling frequency. Modifications are introduced for the traditional turbulent bulk flow model to consider the circumferentially varying flow. A trigonometric series expansion method is used to approximate parameters such as pressure and velocity in seals cavity. Numerical simulations show that 8-10 series terms with 5-10 iterations are enough for the solution of this set of nonlinear equations. The resulting nonlinear algebraic equations can be solved rapidly. The analytical results are verified by comparison with the simulated CFD results. Parametric investigations showing the influence of eccentricity and whirling frequency on seals dynamics are also presented. The results show that the trigonometric series expansion based method gives an effective prediction of the static and dynamic characteristics of the eccentric seals.