The use of composite materials has provided designers with increased opportunities for tailoring structures and materials to meet load requirements and changing and demanding environments. This has led to their increased use in structural applications. As with traditional materials the selection of an appropriate material for a design is important. In case of design using composite materials the selection of a material consists of selecting a fiber-resin combination which meets all design requirements. This involves choosing the fiber, the resin, and the proportion of these two constituents in the composite material. The phrase “material selection” refers to the problem of laminate selection. This corresponds to the task of choosing a fiber and resin combination based on technical and economic factors. Materials tailoring, on the other hand, involves manipulating the composition of the composite material to achieve desired properties and it is the selection of a fiber and resin simultaneously but separately. In this paper we present, through an example, a multiobjective optimization-based method for assisting a designer in tailoring composite materials for specific technical and economic objectives.