A random and discontinuous microstructure is one of the most characteristic features of a low-density thermally bonded nonwoven material, and it affects their mechanical properties significantly. To understand their effect of microstructure on the overall mechanical properties of the nonwoven material, discontinuous models are developed incorporating random discontinuous structures representing microstructures of a real nonwoven material. Experimentally measured elastic material properties of polypropylene fibres are introduced into the models to simulate the tensile behaviour of the material for its both principle directions: machine direction and cross direction. Additionally, varying arrangements of bond points and schemes of fibres’ orientation distribution are implemented in the models to analyse the respective effects.