Torsion of cylindrical shafts has long been a basic subject in the classical theory of elasticity. In 1998 Swanson proposed a theoretical solution for the torsion problem of laminated composites. He adopted the traditional formulation of the torsion problem based on Saint Venant's torsion theory. The eigenfunction expansion method was employed to solve the formulated problem. The analytical method is proposed in this study enabling one to solve the torsion problem of laminated composite beams. Instead of following the classical Saint Venant theory formulation, the notion of effective elastic constant is utilized. This approach uses the concept of elastic constants, and in this context the three-dimensional non-homogeneous orthotropic laminate is replaced by an equivalent homogeneous orthotropic material. By adopting the assumptions of constant stress and constant strain, the effective shear moduli of the composite laminates are then derived. Upon obtaining the shear moduli of the equivalent homogeneous material, the effective torsional rigidity of the laminated composite rods can be determined by employing the theory developed by Lekhnitskii in 1963. Finally, the predicted results based on the present analytical approach are compared with those by the finite element, the finite difference method and Swanson's results.