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Soft conjunctive biological tissues are mainly constituted of fibres. These elastinand collagen fibres can support large strains. For this reason, the commonlyused mechanical behaviors are hyperelastic with anisotropy induced by fibresdistribution. If we want to extend these models to dissipative transformations(damage, plasticity, rupture . . . ) we first have to solve the problem of the definitionof the elastic domain (yield surface).We propose to study the response of an unconnected fibre network submitted toan affine transformation which is a very simple model but often used in literature(see Cox or Sacks for instance). Yield surfaces are then computed using planestresses assumption and considering the fibres as an incompressible material. Theresponses differ a lot from the mechanical behavior of fibres, which could be fragile,damageable or plastic. These results lead to a non obvious macroscopic descriptionof the yield surface.