Differential soil settlements are one of the main reasons of damage in masonry structures. Soil settlements may be caused by different phenomena, such as tunnelling operations, subway construction, underground car parks, soil weakening due to pipe breakage, scouring, etc. The peculiar characteristics of masonry, which include very low resistance in tension and good resistance in compression and shear, make it unsuited to undergo changes in the boundary conditions without the propagation of cracks. The influence of the soil on the structural behaviour is therefore evident, but most of the existing papers treat the problem uncoupling structural and soil responses, which is not the best approach when the settlement is unknown and coupled with the mechanical response of the structure above. Therefore, in this work the problem is studied through a new formulation aimed at explicitly coupling masonry and soil. Masonry is represented through rigid blocks connected by non linear springs, whereas the soil is included as an elastic half-space and is modelled through a boundary integral approach, avoiding mesh discretization issues such as volume discretization and fictitious boundaries at infinity. The processing requires an iterative procedure where the non linear solution of the masonry problems is obtained via minimization of the complementary energy, the reaction forces are transferred to the soil on which the displacement field can be determined and imposed to masonry by updating the boundary condition at the next iteration. After a few iterations, the response of the full system (masonry and soil) is obtained. This method works in three-dimensions and is the extension of a previous work from the first author that was conceived for two-dimensional only problems [1]. Simple three-dimensional examples are shown to prove the potential of the method.