The thesis primarily focused on equi-biaxial tensile testing of materials with hexagonal-based crystal structure such as CP Titanium and Ti-6Al-4V alloy, to understand the influence of stress state on its mechanical properties. In addition, a high strength 7075-T651 aluminum alloy was also chosen, since anisotropy in mechanical properties is reported in this class of material. All the materials studied in this work had a strong preferred crystallographic texture developed during prior deformation and processing. Since, texture in titanium and aluminum alloys largely governs the deformation behavior and the concomitant anisotropic mechanical properties, it is essential to evaluate the mechanical properties of such alloys under complex biaxial stress state. In the present work, cruciform specimen geometry with square gage section optimized using finite element simulations was proposed. Furthermore, the proposed cruciform specimen geometry was validated experimentally using non-contact strain measurement technique vis-à-vis strain homogeneity and attainment of maximum plastic strain in the gage section. Optical and scanning electron microscopic studies were carried out to study the microstructural evolution upon biaxial deformation under equi-biaxial condition. Bulk X-ray texture analysis was carried out to understand the influence of initial texture on the biaxial stress-strain responses of all the investigated materials. The possible deformation mechanisms operating under biaxial stress state was deduced from the texture transition studies. The fractographic analysis was carried out on tested samples to understand the influence of stress state on the fracture behavior of all the tested alloys. Finally, the biaxial deformation behavior of all the investigated materials were compared and contrasted, and the observed differences in their stress-strain responses were correlated to the underlying initial texture in the as-received condition.