In this paper we consider a flexible woven composite materials with plain weave reinforcing fibers and vinyl matrix. The main features of these materials are a geometric nonlinearity and a complexity of their microstructure. Flexible woven composites differ in architecture of plain weave, the percentage of reinforcing fibers and their thickness. The paper puts forward micromechanical structural model describing the complete diagram of deformation of the flexible woven composites under uniaxial tension. The model is laminated with the inelastic deformations. A periodically repeating element was detached, and then it was divided into sub-elements. The strain energy was calculated at each structural element and then it was used to calculate displacements according to the Castellano theorem. The article exemplifies modeling of preliminary damage to the material, and the influence of damage on the stress-strain diagram was analyzed. The damage was introduced by changing in the topology of geometry of reinforcing strands, the change correlating with certain residual deformations. This model is universal for any flexible composite woven plain weave. The simulation results were compared with experimental ones, and the model demonstrated a good fit to the data mentioned and minimum errors.