Constitutive description of deformations in technical textiles mostly requires some highly nonlinear material law due to the interaction between the orthotropic yarns and the effect of the matrix. Phenomenological models aim to garb the overall (macro level) behavior required for engineering purposes. This paper introduces a new, two-dimensional phenomenological model for technical textiles accompanied with a data acquiring strategy to determine the material parameters involved in the model. It handles the nonlinear stress-strain relation observed in uniaxial tests and take the interactions in the two, orthogonal directions into account. As we aim to introduce a solution applicable at the service level of the loads, our model is inherently elastic, no time dependent or plastic behavior are introduced. The model can be solidly fit to the measured data.