Repeated small amplitude dynamic loading of the soil in the vicinity of buildings, as arising from traffic or construction activities, may cause differential foundation settlements and structural damage. In this paper, an accumulation model for settlements due to vibrations at small strain levels in granular non-cohesive soils is proposed. It is assumed that the dynamic part of the stresses is small with respect to the static part. As plastic deformation in the soil is only observed after a considerable amount of dynamic loading cycles, only the accumulation of the average plastic deformation is considered. The accumulation model is calibrated by means of cyclic triaxial tests. However, the stress conditions in the cyclic triaxial tests are an approximation of the complex loading paths in the soil under traffic induced vibrations, that are intrinsically multi-axial and transient signals. Therefore, a rainflow counting algorithm is used to relate traffic induced vibrations to the triaxial test conditions. The model is applied to compute the differential settlement of a two-story building founded on loose sandy soil under repeated passages of a truck on a nearby speed table. Results demonstrate that vibrations may give rise to significant long term settlement of structures.