A simple two-dimensional model for the deformation of auxetic microporous polymers (those with a negative Poisson’s ratio) has been developed. This model network of rectangular nodules interconnected by fibrils has been further developed to include the possibilities of fibril hinging, flexure and stretching. Expressions for strain-dependent Poisson’s ratio and Young’s modulus have been derived and compared with experimental results on microporous PTFE and UHMWPE. A combination of the hinging mode followed by the stretching mode of deformation can be used to explain the general features of the experimental data for these auxetic polymers. The force coefficients governing the different modes of deformation are dependent on fibril dimensions and intrinsic material properties. By varying the geometry of the network, the model can be used to predict different combinations of Poisson’s ratio with modulus, from large positive through to large negative values.