The features of finite element modeling of both an element itself and its behavior under uniaxial tension have been demonstrated with a structural element of flexible woven composites. The main material partials such as reinforcing fabric and material’s matrix were examined in modeling. The reinforcing fabric is a plain weave. These threads were taken as an elastic material. The matrix of the material was considered as a soft polymer with the possible occurrence of irreversible elastic-plastic deformations. Moreover, the possible occurrence of damages in the structure of the material under high loads was taken into account in modeling. The fields of stresses and strains were built; the zones of material internal damages under uniaxial tension were demonstrated. The risk zones of weave were revealed.