The objective of the paper is to analyze four point bending tests performed on samples of an epoxy-type thermoset polymer oxidized under several conditions, and to predict the failure mechanisms. Different responses are observed depending on the oxidation time: for small durations there is a linear elastic phase followed by an abrupt failure of the specimen whereas for higher oxidation times, the elastic phase is followed by a nonlinear one corresponding to the development of numerous superficial micro-cracks prior to failure. In order to predict this behavior, a finite fracture mechanics approach based on the coupled criterion is used. This criterion requires an energy and a stress condition to be fulfilled. This approach is here extended to take into account the gradient of properties of the oxidized layer: Young " s modulus, tensile strength, toughness. One novelty of the approach is to implement the model in a periodic representative cell in order to process an increasing number of cracks. Despite the large scattering in the experimental detection of the initiation of the micro-cracks and their counting, the predictions agree rather well with the observations: the oxidation times leading either to a sudden failure of the sample or to micro-cracking are well reproduced, and the loads triggering the crack onset as well as the increase in number of cracks are somewhat well predicted.