AbstractUnderstanding the mechanical properties of membrane materials in two-dimensional (2D) stress space is critical for structural design and mechanical analysis of membrane structures. In this paper, an experimental study of the warp-knitted fabric PVDF8028 subjected to biaxial loads was performed to expose the detailed mechanical behaviors and determine proper elastic parameters for the fabrics under multiple stress ratios. The least-square method was adopted to calculate the elastic parameters for different stress states, and response surfaces of strain and elastic parameters were used to reveal the mechanical behaviors in detail. Comparison between coated plain-woven and warp-knitted fabrics was used for exhibiting the influences of microstructures and deformation mechanisms on the macroscopic mechanical properties of materials. The results show that the stress–strain behaviors exhibit significant nonlinearities, and could be characterized by appropriate response surfaces. The elastic stiffness response surfaces of loading and unloading processes could form an unbalanced X-shaped cross, and detailed elastic parameters in those two processes could be obtained by corresponding response surfaces. Compared with plain-woven fabrics, warp-knitted fabrics could exhibit more obvious nonlinear characteristics due to the existence of their coiled yarns and lower Poisson’s ratios because of the special noncrimp yarn structure. The differences in macroscopic mechanical properties for these two materials result from the corresponding differences in microstructures and deformation mechanisms.