The objective of this research is to propose a mathematical model of deformation of textile composite materials based on aramidfabric under shock action. The model takes into account the following deformation parameters of composite materials of the specified class: the ability to change their forms without destruction at finite deformations, a considerable difference between stress-deformation diagrams under tension and under compression, dependence of these diagrams on a loading rate, pseudo-plastic properties of materials caused by pulling out threads from fabric, anisotropy of nonlinear-elastic and viscous-plastic properties and other effects. Additionally, we took into consideration viscous-elastic properties of the aramid fibers, damageability and fiber breakage when punching the textile materials. Thus, we stated the problem of dynamic deformation of textile composite materials. In order to solve the problem, we applied the method of band-adaptive grids in a two-dimensional case. We give an example of computational solution of the problem, which involves a high-speed action of a striker onto a textile composite material. In conclusion, we compare the computational modeling and experimental results in punching the aramid textile composite materials.