In this paper, the wave characteristics, divergence stability and dynamics of the oil pipelines conveying internal flow are investigated by using the spectral element method which has been known as the exact solution method. The spectral element model is formulated from the governing differential equation of motion transformed into the frequency-domain by using the discrete Fourier transform theory. The internal flow velocity at which the divergence instability occurs is derived in an analytical form. Numerical studies are conducted to investigate the wave characteristics, divergence stability and dynamics of an oil pipeline depending on its viscoelasticity and internal flow velocity. (C) 2008 Elsevier Ltd. All rights reserved.