This paper deals with a detailed, three-dimensional stress and displacement analysis of transversely loaded, laminated complete hollow cylinders and open cylindrical panels having a symmetric or an antisymmetric cross-ply lay-up. The analysis is based on a refined, static version of a successive approximation approach which was first proposed by Soldatos and Hadjigeorgiou (J. Sound Vibration 137 (1990) 369-384) in connection with corresponding dynamic problems. However, the present refined formulation makes use of a recursive rather than a successive approximation formula. As a result, independently of the number of layers employed, the solution of the bending problem considered always ends with the solution of a sixth order system of simultaneous algebraic equations. The effectiveness of the approach employed is checked by comparing numerical results with corresponding three-dimensional elasticity results published elsewhere in the literature. Then, the proposed formulation is further used towards a detailed stress and displacement analysis of the afore-mentioned structural elements.