Cylindrical shells find wide applications in many engineering fields. Free vibration analysis of cylindrical shells filled with fluid has been dealt using finite element approach for both structure and fluid domain or using finite element for structure and Bessel function approach for fluid. The present paper deals with a novel method on the usage of polynomial functions for fluid domain in contrast to the usual Bessel function approach. A semi-analytical finite element approach has been used to discretise the shell structure. The fluid domain has been analysed by using polynomial functions instead of Bessel function. The study has been carried out for conventional shells as well as viscoelastic shells. The present study obviates necessity of limiting the studies to certain boundary conditions. The results of both frequency and damping corroborate well with those found in literature. © 2005 Elsevier Ltd. All rights reserved.