A simple strain-based yield/failure criterion for fiber composite materials is incorporated into a kink band analysis of compressive failure. Under realistic conditions of fiber misalignment the analysis predicts compressive failure at load levels about one–fifth of the ideal value, and with kink band inclinations of about 20 deg. Some parametric variations of the relevant physical variables are given in simple graphical forms, and comparisons are made with newly obtained micrographs of kink bands.