Inverse methods have considerably facilitated the identification of complex responses, and hence permitted to represent more realistic behaviours. We have developed and applied a specific identification strategy in order to characterise the strongly nonlinear surface response of knitted elastomeric fabrics undergoing large biaxial deformations (>80%). These particular orthotropic materials are used for medical applications, delivering limited mechanical efforts, but which strongly depend on the fabric biaxial state of stretching. The identification procedure relies both on FE simulations using a corotational formulation, and on a full-field measurement optical method able to characterise the displacement fields under biaxial tension. A Levenberg-Marquardt algorithm is then used to identify the surface response coefficients for our fabrics, by comparing the distance between experimental and numerical results in the sense of nonlinear least-squares. This comparison requires to characterise both FE and experimental displacements/forces at the same points, which were chosen as the geometrical (fixed) points experimentally used. For the identification, several scalar and field input data were tested, it appears that the procedure is regularised by adding the global displacement comparison to the full-field displacements comparison. Eventually, the identified surfaces are shown to well-represent the fabric response for strain ranges of practical medical use.