The close,j-form analytic expressions for the di.aplacement and stressas at any point of either of two differently coupled orthotropic elastic half-spaces due to a vary long vertical strike-slip dislocation situated in the upper elastic half-space have bean obtained.The interface between two semi-lnfinite media is assumed to be horiZontal and parallel to one plana of elastic symmetry of the orthotropic elastic medium. The coupling between two semi-infinite media is assumed to be either ‘welded’ or ‘smooth-rigid’ or ‘rough-rigid’. The variations of the displacement and stresses with the horizontal distance from the fault are compared to study the effect of the different types of the coupling. It is found that the horizontal displacement for ‘welded’ coupling lies between the corresponding displacements for the ‘rough-rigid’ and ‘smooth-rigid’ couplings for different positions observer.