Abstract A method for calculating the stresses in a notched monolayer of unidirectional, filamentary composite is described. This numerical formulation permits the modeling of a finite dimensioned monolayer which contains a centered notch transverse to the fibers. Tractions or displacements parallel to the fibers and elastic work-hardening constitutive relationships for the fibers and/or matrix may be specified. Slow notch growth can be analyzed by the method presented. Illustrative calculations for a boron/aluminum monolayer identify widespread matrix yielding and a notch-fiber stress concentration whose magnitude depends on the nature of the work-hardening matrix. When applied to center-notched, multilayered, unidirectional boron/aluminum, this model predicts a nonlinear response of the notch opening displacement to load. It also predicts the matrix yielding in regions remote from the notch tip. Each of these predictions has been confirmed by experiments. The model is also able to provide reasonable estimates of notched composite failure strength.