This work verses about determination of failure envelopes of unidirectional fiber reinforced composites. A two scale analyses is considered and the mathematical theory of the asymptotic homogenization technique is applied to model the problem. The structure in analysis is the macro scale and the micro scale is represented by a heterogeneous periodic unit cell that is regarded periodic within the macro scale domain. Given the elastic properties of the constituents (fiber and matrix), the mathematical model is capable of predicting effective elastic properties of composites. The accuracy of the technique in predicting elastic properties of composite materials is measured by comparing numerical effective properties to experimental properties and it revealed good correlation to the experimental data. Also, with this technique, it is possible to assess stresses at its micro level for a given stress applied to the macrostructure. A methodology to determine failure envelopes is proposed in this work. In the failure study, three regions of the composite are considered: matrix, fiber and the interface between them. Each region is governed by its own failure criterion. Given only five unidirectional strengths of the composite, the strengths of each region are calculated and the failure envelopes can be built. To validate the methodology, the numerical failure envelopes are compared to failure envelopes experimentally obtained and good correlation was observed.