Engineering textile composites are built of a polymeric resin matrix reinforced by a woven fabric, commonly glass, kevlar or carbon fibres. The woven architecture confers multidirectional reinforcement while the undulating nature of fibres also provides a certain degree of out-plane reinforcement and good impact absorption; furthermore, fibre entanglement provides cohesion to the fabric and makes mould placement an easy task, which is advantageous for reducing production times. However, the complexity of textile composites microstructure, as compared to that of unidirectional composites makes its mechanical characterization and design process a challenging task, which often rely on well-known failure criteria such as maximum stress, maximum strain and Tsai-Wu quadratic interaction to predict final failure. Despite their ample use, none of the aforementioned criteria has been developed specifically for textile composites, which has led to the use of high safety factors in critical structural applications to overcome associated uncertainties. In view of the lack of consensus for accurate strength prediction, more experimental data, better testing methods and properly designed specimens are needed to generate reliable biaxial strength models. The aforementioned arguments provide motivation for this thesis, which presents the development of an improved cruciform specimen suitable for the biaxial tensile strength characterization. A glass-epoxy plain weave bidirectional textile composite is here selected as study case, as a representative material used on many industrial applications. The developed cruciform specimen is capable of generating a very homogeneous biaxial strain field in a wide gauge zone, while minimizing stress concentrations elsewhere, thus preventing premature failure outside the biaxially loaded area. Seeking to avoid in-situ effects and other multilayer-related uncertainties, the specimen is designed to have a single-layer gauge zone. This is achieved by a novel manufacturing process also developed in this research, which avoids most drawbacks found in typical procedures, such as milling. Once the suitability of the specimen was demonstrated, an original biaxial testing machine was designed, built, instrumented and calibrated to apply biaxial loads; the apparatus included a high definition video recorder to get images for digital image correlation strain measurement. An experimental tests program was then conducted to generate a biaxial tensile failure envelope in the strain space. Based on the experimental results, a phenomenological failure criterion based on experimental results and physical textile parameters such as the number of layers and unit cell dimensions was developed. The predicted failure envelope predicted by this criterion achieves very good agreement with the experimental data.