This paper presents the free vibration analysis of stiffened coupled shear walls with flexible foundations based on a discrete-continuous approach, where the structure is considered as both a discrete system and a continuous system at different stages of the analysis. The stiffnesses of the flexible foundations are represented by rotational and translational springs at the base of each shear wall. The stiffened system is reinforced by an additional stiffening beam at some level of the structure. This induces additional axial forces, and thus reduces the bending moments in the walls, as well as helping to reduce the lateral deflections and increase the natural frequencies. The effects of foundation stiffnesses and the stiffening beam on the free vibration characteristics of the structure are investigated. The optimal position for the stiffening beam to increase as far as possible the first natural frequency of vibration is also presented.

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