a b s t r a c tThe optimal design of composite structures with frequency-dependent interleaved viscoelastic damping layers is addressed in this paper. The design objective of simultaneously maximizing structural modal damping and frequency and minimizing weight is considered. The design problem is formulated as a mixed integer multi-objective optimization problem and solved by evolutionary algorithm. A layerwise finite element model is used. The Pareto-optimal solutions are obtained for two applications. The results show that the approach is quite useful in integrally designing such kind of composite structures. In particular, it is shown that the inserting position and the material type are two important design parameters.