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The computer algebra system MATHEMATICA is used for the solution of classical torsion problems in the theory of elasticity together with the energy of variational method (or even, equivalently, the Ritz method). The cases of an elliptic, a triangular and a rectangular cross-section are studied. Although the first two cases lead easily to exact results, more important is the third case, where SAN (semi-analytical/numerical) approximate results are obtained. These results incorporate the dimensions of the rectangular cross-section as well as all additional symbolic quantities. The same results are also seen to converge to the corresponding numerical results for particular numerical values of the dimensions of the cross-section. Generalizations of the present results are also briefly proposed.
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