This paper presents a numerical methodology to analyze frame structures supported on footing foundations subjected to slow strains caused by consolidation settlements. A building project on a subsurface layer of soft soil has been analyzed. The Boundary Element Method with the Mindlin fundamental solution has been applied to compute the displacement resulting from the interference between pressure bulbs on the foundation. The rheological Kelvin–Voigt model has also been used for soil–structure interactions. Terzaghi’s Theory of Consolidation was used to fit the displacement–time curves. Finally, the rheological model was coupled through an iterative procedure, employing structural non-linear geometric effects. The results are consistent with settlement predicted effects and revealed that the slow distribution of efforts can cause relevant increases in some regions in the structure of the building.