Fibers of linear polymers below the glass transition show a strong nonlinear deformation behavior even at small strains. The elastic modulus is a fast increasing function of the strain. A new model for the description of the deformation of these fibers is presented. It is assumed that the fiber consists of long and continuous polymer chains which do not break during the extension of the fiber. The deformation of the fiber is calculated for finite strains and arbitrary values of the orientation parameter. Equations for the elastic stress versus strain curve and modulus versus strain curve have been derived. The model can be used for the calculation of the modulus of isotropic fibers and sheets with uniplanar orientation as well.