Abstract: Composite structures with interleaved viscoelastic layers have favorable damping properties, but viscoelastic layers may weaken their strength. They can meet the needs of engineering requirements when composite structures with interleaved viscoelastic layers have both favorable damping properties and higher strength properties. Based on the classical laminate theory or the small deflection theory, mathematical models are built for a loss factor of strain energy and first-ply failure strength under uniformly lateral distributed loads by the Ritz method. A novel function of adaptive genetic algorithms is proposed to overcome the excursion phenomenon of multiobjective optimization. The optimization designs of single objective and multiobjective are investigated for the materials. The numerical results show that the modified genetic algorithm is available for optimization design of a loss factor and strength. The multiobjective optimization design is used to balance their properties between damping and strength. It is beneficial to improve the multiple mechanical properties of composite structures with interleaved viscoelastic layers.