Abstract: It is well known that structural behaviors of composites are dictated by micro configuration and macro arrangement of microstructure. A multi-objectives optimization design model integrating materials and structures in consideration of static and dynamic performances for periodical composites is presented and related numerical experiments are carried out. In the model, the optimization objects are to maximize the structure fundamental frequency and minimize the structure compliance. RAMP (Rational Approximation of Material Properties) is adopted to ensure clear topologies in both macro and micro scales and design variables for macrostructure and microstructures are defined separately and integrated into one system by using the super-element technique. In addition, to improve the smoothness of the objective function and avoid the singularity of numerical computation, the weighted objection function is normalized. On the basis of the numerical experiments, the effects of the weighted coefficient of the static and dynamic optimization on the topology form and objective values (the structure fundamental frequency and compliance) are investigated. The results indicate that the proposed method is effective and can be used as an innovative design concept for lightweight structures.