Textile facades have become increasingly important in modern architecture, especially in sports facilities, due to their lightweight, appealing aesthetics, and energy efficiency. Precise prediction of their nonlinear viscoelastic creep behavior is essential to ensuring both durability and optimal performance over time. This research presents a nonlinear viscoelastic material model implemented in Abaqus through a UMAT subroutine, developed using experimental data from prestressed textile facades. Numerical simulations closely replicate experimental results, accurately predicting deformation and stress relaxation under realistic loading conditions. The study analyzes vertical and horizontal displacements, emphasizing Poisson’s ratio, which describes the material’s inherent tendency to deform laterally when stretched axially, maintaining near-constant volume and contributing to shape preservation. This enhanced understanding supports the creation of reliable, cost-effective design methodologies for durable textile facades, advancing sustainable and smart architecture in civil engineering. These results emphasize the potential of textile facades for innovative construction solutions, where accurate modeling of viscoelastic behavior allows architects and engineers to fully leverage textile materials’ unique structural and environmental benefits.