The simulation of the mechanical behaviour of structures with the finite element method is one of the main tasks in engineering mechanics and requires both constitutive and structural parameters. In addition to a qualified geometrical approximation of the structure with the finite element discretization and the definition of initial and boundary conditions it is necessary to select material models for the realistic description of the mechanical system at hand. Furthermore, the material models chosen require reliable numerical data for the associated constitutive parameters, which are usually not known for most new materials like reinforced composites, if their properties are not listed in a database or if they consist of different constituents. Composites usually possess unknown microstructural properties, which cannot be assigned to typical specimen of homogeneous material distribution. Due to the imperfect manufacturing process the mechanical behaviour of composites can significantly vary and the associated material parameters must be determined from the overall behaviour of the composite. Therefore, the unknown material parameters, as the essential input data for the consitutive model for every finite element simulation, must be identified by solving an inverse problem before the complete structure is analyzed.