This work deals with the evaluation of mutual coupling in arrays of apertures or printed radiators and other similar problems. Two analytical-based numerical integration techniques will be described, for the efficient evaluation of the spectral reaction integrals between two arbitrary functions on separated domains in a general stratified medium. These techniques employ novel schemes of contour deformation. The spectral domain formulation is used, and integration is carried out in Cartesian coordinates, taking the x axis along the direction adjoining the centers of the two basis functions involved. In both techniques the kx contour is deformed along the negative imaginary axis in order to turn the oscillating shift exponential into a decaying term. A robust scheme is obtained, with yet additional advantages in the case where many coupling terms at different distances are to be evaluated (as in alignments within arrays). Validation against published data and an application example are presented, along with a discussion of the numerical performances. ¿ 2000 American Geophysical Union