Axial instability of rimming flow has been investigated by solving a linear generalized eigenvalue problem that governs the evolution of perturbations of two-dimensional base flow. Using the Galerkin finite element method, full Navier-Stokes equations were solved to calculate base flow and this base flow was perturbed with three-dimensional disturbances. The generalized eigenproblem formulated from these equations was solved by the implicitly restarted Amoldi method using shift-invert technique. This study presents instability curves to identify the critical wavelength of the neutral mode and the critical beta, which measures the importance of gravity relative to viscosity. The axial instability of rimming flow is examined and three-dimensional flow was reconstructed by using eigenvector and growth rate at a critical wave number. The critical beta value in the axial instability analysis was observed to be comparable to the onset beta value of the transition between the bump and the homogeneous film state in 2-D base flow calculations. Copyright (c) 2006 John Wiley & Sons, Ltd.