A 2D model for the deformation of auxetic microporous polymers (those with a negative Poisson’s ratio) has been previously developed, consisting of a network of rigid rectangular nodules interconnected by fibrils. This model has now been extended to describe the deformation of the network via concurrent fibril hinging and stretching mechanisms. Expressions for the strain-dependent Poisson’s ratios and Young’s moduli are derived and fully investigated with respect to their dependence on the model parameters. These expressions are compared with the experimental strain-dependent data for auxetic microporous polytetrafluoroethylene (PTFE) and ultra-high molecular weight polyethylene (UHMWPE). The use of concurrent deformation mechanisms makes a very significant improvement in the agreement of theory with experiment for both cases. Slight discrepancies are discussed in terms of the use of the assumptions of a 2D network of regular, rectangular nodules and a constant force coefficient ratio governing the two deformation mechanisms.