In this work a study of pneumatic structures considering pressure–volume coupling under plastic and viscoplastic material behavior is developed. Pneumatic structures are membrane structures acted on by air or gases stabilized by tension. These structures are lighter than conventional structures resulting in economic structural solutions. They present also some characteristics that contribute to the sustainable development, such as the utilization of natural lighting and ventilation and its possibility of reuse. When pneumatic structures are subjected to external loads these structures present both internal pressure and volume variation. This coupling is one of the objects of the present work. Analytical solutions are developed to describe this coupling. In conventional finite element systems this coupling is not considered. A formulation for pressure–volume coupling by closed chambers is included in the framework of a finite element large strain model. The variety of material models implemented has the purpose to cover the behavior of the many kinds of membrane materials used in pneumatic structures. In the literature the study of the membrane materials for pneumatic structures focuses on experimental analysis. Membrane material models are incorporated in the finite element model for small and large strains. The constitutivematerial models considered in this work are hyperelastic, elastoplastic and elastoviscoplastic. The onset of large strains is enclosed. A new material model based on NURBS surfaces is proposed an validated on hand of experimental results and classic material models. In this work emphasis is given to the material ETFE (Ethylene tetrafluoroethylene), which is widely used in pneumatic structures. The models developed here, such as the pressure-volume coupling and the material models, are implemented in finite elements on the program used in the Static Chair at TUM (Technische Universitat Munchen), which is called CARAT++ (Computer Aided Research Analysis Tool).