A novel approach to analyze kink banding failure in fiber reinforced composites is presented in this paper. By considering a single fiber–matrix unit cell and utilizing a fiber deformation representation that can simultaneously account for instability due to increasing fiber amplitude and fiber rotation, a sequence of events that lead to the formation of a kink band is elucidated. It is shown that peak compressive strength does not necessarily correspond to the onset of yielding (non-linearity) in the matrix and is dictated by the interaction between matrix non-linearity and initial fiber misalignment. Predictions of compressive strength and kink band formation, utilizing the new model, are found to be in good agreement with reported experimental data and associated higher-order finite element analysis.