The state of stress in a beam of circular cross-section simply supported and loaded in the mid-span is considered as the non-axisymmetric problem of a cylinder within the framework of the three dimensional theory of elasticity. In this analysis, Dougall's stress function approach is used and boundary conditions are satisfied by use of the Fourier integral transforms. In this case, the stresses on the surface are expressed with divergent series including divergent integrals, but by eliminating the divergent terms and using Shanks' acceleration method, numerical calculations are carried out. The validity of the elementary beam theory is examined in comparison with the results thus obtained.
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