A procedure for the evaluation of the double integrals involved in the symmetric BE method is proposed, which consists in a regularization via integration by parts and in a successive numerical evaluation of weakly singular integrals. The procedure is applicable to curved elements and higher order shape functions and lends itself to a fairly straightforward implementation. Continuity is required for displacement modelling, while tractions may be modelled as piece-wise continuous. Some example problems characterized by the presence of curved boundaries or of cracks are analyzed using the proposed technique to demonstrate its effectiveness.