The problem of stabilization of a system of coupled PDEs of the forth-order by means of boundary control is investigated. The considered setuparises from the classical Euler-Bernoulli beam model, and constitutes ageneralization of flexible mechanical systems. A linear feedback controlleris proposed, and using an abstract formulation based on operator semi-group theory, we are able to prove the well-posedness and the stability ofthe closed-loop system. The performances of the proposed controller areillustrated by means of numerical simulations.