A refined formulation of an approach suitable for three-dimensional vibration analyses of homogeneous and cross-ply laminated cylinders and cylindrical panels (Soldatos and Hadjigeorgiou, 1990, J. Sound. Vibr. 137, 369-384) is presented. Based on a recursive rather than a successive approximation formula, the present refined formulation always makes use of a 6 x 6 frequency determinant, regardless of the number of layers of the laminated shell or panel considered. Upon comparing its results with corresponding numerical results available in the literature, the effectiveness of the approach in producing the exact frequencies of vibration is checked. Moreover, further detailed numerical results dealing with flexural vibration frequencies and corresponding mode shapes of laminated cylinders and cylindrical panels having symmetric or regular antisymmetric cross-ply lay-up are presented, studied and discussed.