The modelling of dry knitted reinforcements for structural composite parts at the mesoscopic scale is essential to establish simulation tools related to shaping processes. Deformation modes of such structures are linked to the textile's manufacturing process, resulting in an anisotropic heterogeneous structure. This observation leads us to build an accurate 3D parametric geometric model of a jersey knit. Based on this geometric model, a finite element model is generated, allowing the analysis of the biaxial tensile mode of the elementary cell. In order to update the constitutive behavior, two formulations are implemented in the code Abaqus/Explicit and take into account a yarn's compaction law and the evolution of the constitutive axes as large deformations occur. Finally, a comparison between the results of the two formulations and an experimental test is proposed.