Writing the boundary integral equation for an exterior problem of elasticity is subordinate so far to hypotheses on the asymptotical behaviour at infinity of solutions. The sufficient conditions met in the literature are too restrictive and do not notably cover the case when the loading has a non zero resultant force. This difficulty can be removed by considering the problem in displacements relatively to one point located at a finite distance from the loading. Finally, this auxiliary problem allows widening the conditions of validity of the usual formulation of the direct integral method.