This paper addresses the problem of designing robust stabilizing controllers for a class of cable-stayed flexible structures. The dynamic behaviour of the structure is characterized by a beam decomposed into a finite number of concentrated masses. The mathematical model exhibits uncertainties in parameters, stay cable geometry and couplings, as well as in the unknown environmental excitation. The controller design is made based on the principle of sliding mode to reduce the magnitude of the transverse vibrations of the structure induced by the environmental excitation. A numerical simulation example is presented to illustrate the effectiveness of the proposed control scheme.