Center-notched and unnotched specimens cut from Celion 3000/PMR15 woven composite panels with 60% fiber volume fraction were tested under quasi-static compressive load to failure at room temperature. Micrographic evidence clearly identifies the mode of compressive failure as fiber kinking. Each fiber in the kink fractures because of a combination of compressive and shear stresses. A post failure mechanism follows the local fiber bundle failures, which completely deforms the material by large cracks. ln center notched specimens, fiber kinks start from the notch and propagate to some distance from the notch before the post failure takes place. The effect of bundle interactions on stresses and strains was clearly distinguished by comparing the results of the finite element analysis of a bundle surrounded by other plies to the results of the Moire interferometry on the edge of a laminate. A model was introduced which incorporated the micromechanical geometry as well as the constituent properties to predict the notched and unnotched compressive strengths of the woven material. For notched strength predictions, the Average Stress Criterion was used, and the characteristic distance was found to be a function of laminate thickness. Predicted notched and unnotched strengths correlate very well with the experimental results.