In this study shape optimization of fibers in composite fiber reinforced structure is presented. The problem targets the optimal shape with respect to the maximum bearing capacity and the minimum deformation of the whole composite set up. The shape is constrained by a constant volume (area) ratio. The optimization includes a process of seeking the overall properties of composites, i.e. localization and homogenization. Since no a priori estimate of the shape of fibers is known, numerical tool, finite element method, is employed. Such a problem is important in a wide range of applications, prevailingly in fiber reinforced concrete assessment, biomechanics, biophysics, and in the mechanics of classical composites with epoxy matrix. Since many types of fibers are used in various fiber reinforced concretes (fibers from polypropylene, steel, glass, clay, basalt, hemp, etc.), a deeper study is of importance to engineers and researchers. Application on FRC is preferred, i.e. fiber volume ratio is small, while classical composites require relatively very high volume ratio. The theory involves an original procedure leading to the optimal shape of fibers; it is then applied in the form of a numerical study. Also two examples from experiments verify the theoretical results. The problems are solved as two-dimensional, i.e. a unidirectional distribution of fibers is supposed., Petr P. Procházka and Martin Válek., and Obsahuje bibliografii