Although variational Galerkin-type boundary integral formulations have received a lot of attention, mostly in the applied mathematics field, they have led to relatively few developments and applications in the field of solid mechanics, compared to the very popular collocation boundary element methods (CBEM). Usually variational methods involve double surface integrals. Variationnal approaches have nevertheless attractive conceptual features over usual collocation methods: known convergence results are more extensive and actually better than those of CBEM, and they lead to symmetric stiffness-like BEM matrices. Moreover, as it will be seen below, the variational traction boundary integral equation (TBIE) requires $C^{0,\alpha}$ interpolation of the densities instead of $C^{1,\alpha}$ at the collocation point for the collocation TBIE. The usual $C^0$ conformal shape functions may then be used. On the other hand, the implementation of this approach for general engineering problems is somewhat more involved than using collocation, which explains perhaps its relative lack of popularity.