A recently introduced nonlocal peridynamic theory removes the obstacles present in classical continuum mechanics that limit the prediction of crack initiation and growth in materials. Furthermore, damage growth in composites involves complex and progressive failure modes. Current computational tools are incapable of predicting failure in composite materials mainly due to their mathematical structure. However, the peridynamic theory removes these obstacles by taking into account non-local interactions between material points. This study presents an application of the peridynamic theory for predicting damage progression from a central crack in fiber reinforced composite plates subjected to uniaxial tension loading.