A very succesful approach for the assesment of failure properties of material, called fracture mechanics, has been developed in last decades. The requirement of existence of at least one identifiable crack causes that fracture mechanics is not able to predict the failure by a simple tensile test. Hence the substantial difference is made between the approach of fracture mechanics and that of damage mechanics. The origin of such difference was motivated by the necessity of describing the behaviour of materials containing system of voids. The basic goal of the damage mechanics concept is to solve a relationship between the failure of the material and its inner structure. Two-dimensional models of the mechanical properties of textiles can be used to study the process of the material failure [1,2]. The influence of the mechanical inhomogenity of the models on stress-strain curves in uni-axial deformation and on the process of cracks origin and growth is shown in the paper.