An investigation is described of the free vibration characteristics, i.e., natural frequencies and damping ratios in flexural modes of cylindrical tubes made from fibre reinforced materials with potential usage as composite shafts. This paper is concerned with only the first circumferential modes, which are essentially the beam bending modes. The results obtained from beam and shell theories are compared, which leads to the determination of limits of tube parameters up to which beam theory gives valid results. Viscoelastic material damping has been assumed and system loss factors have been determined for various modes, by using the complex modulus approach in the beam and shell theories. The results obtained indicate that for practically used tube parameters, flexural frequency values obtained from beam theory with Timoshenko type shear deformation match well with those from shell theory without thickness shear deformation. The closeness of the results from the two theories improves further when the shell theory accounts for thickness shear deformation. In comparing the results obtained from beam theory and shell theory, emphasis is given to possible explanations of the points of difference in terms of physical behaviour of the shell. © 1994 Academic Press Limited.