This paper presents an improved dynamic analysis for liquid annular seals with arbitrary profile based on a method first proposed by Nelson and Nguyen. An improved first-order solution that incorporates a continuous interpolation of perturbed quantities in the circumferential direction is presented. The original method uses an approximation scheme for circumferential gradients of zeroth order solution based on Fast Fourier Transforms (FFT). A simpler scheme based on cubic splines is found to be computationally more efficient, with better convergence at higher eccentricities. Arbitrarily varying seal profiles in both axial and circumferential directions are considered. A procedure for computing dynamic coefficients based on external specific load is discussed. An example case of an elliptical seal with varying degrees of axial curvature is analyzed. A case study based on actual operating clearances (6 axial planes with 68 clearances/plane) of an interstage seal of the Space Shuttle Main Engine High Pressure Oxygen Turbopump (SSME-ATD-HPOTP) is presented.Presented in the 48th Annual Meeting in Calgary, Alberta, Canada May 17-20, 1993