A method for evaluating the functionality of polymer textile materials with the purpose of increasing their competitiveness is presented. The functionality of polymer textile materials is assessed based on mathematical modeling of their viscoelasticity. To that end, a widely-recognized approach to mathematical modeling of viscoelasticity of polymer materials is considered. This approach involves an analytical approximation of experimental families of relaxation and deformation curves by normalized relaxation and deformation functions on a logarithmic scale of reduced time.