Composite materials are increasingly being used in load bearing structures due to their high specific stiffness and strength. Designing composite structures involve solving multiple conflicting objectives (e.g weight and deflection) and constraints (e.g failure stress and strain), which is a challenging task. In the absence of an optimal solution, a compromise solution is desired. Concurrent (material selection plus sizing) design approach using Decision Support Problem (DSP) is used to arrive at a compromise solution. In this paper multiscale design approach is proposed, that incorporates the tailoring of material microstructures and sizing to achieve improved compromise solution. The microstructure properties are obtained by using analytical and computational models for various composite materials. These models compute structure-property relations between bulk material properties and their micro-structural constituents. The approach is demonstrated with an example of a sandwich composite cantilever beam subjected to multiple load cases. An efficiency factor (η) is defined to compare the results of concurrent design approach and multiscale design approach.