The formal application of the Fourier integral transform is shown to give rise to divergent integrals in the solution of Flamant's problem of the classical theory of elasticity. To avoid the occurrence of such divergent integrals, a second generalized Fourier transform is proposed and made use of (the first one in this area is due to Golecki [1]). This second generalization to the Fourier transform is the appropriate one for attacking elastostatic boundary value problems through the representation, due to Sneddon [2], of the displacement vector in terms of harmonic functions instead of through Airy's stress function.