Due to random orientation of fibres and presence of voids in their microstructure, low-density thermally bonded polymer-based nonwovens demonstrate complex processes of deformation and damage initiation and evolution. This paper aims to introduce a micro-scale discontinuous finite element model to simulate an onset of damage in low-density nonwovens. In the model, structural randomness of a nonwoven fabric was introduced in terms of orientation distribution function (ODF) obtained by an algorithm based on the Hough Transform. Fibres were represented in the model with truss elements with orientations defined according to the computed ODF. Another structural element of nonwovens - bond points - were modelled with shell elements having isotropic mechanical properties. The numerical scheme employed direct modelling of fibres at micro level, naturally introducing the presence of voids into the model and thus making it suitable for simulations of low-density nonwovens. The obtained results of FE simulations were compared with our data of tensile tests performed in principal directions until the onset of damage in the specimens. (C) 2012 Elsevier B. V. All rights reserved.