The aim of this research is to gain more understanding of the physics of the transportation of materials having viscoelastic characteristics, high transport speeds, a small thickness and a large surface area. This study introduces new models that take into account both material viscoelasticity and the fluid-structure interaction between the travel- ling material and the surrounding owing fluid. A web (continuum) travelling between two fixed supports is considered, modelling the web as a Kelvin–Voigt type viscoelastic panel and the air ow as a potential ow. Stability of the system is studied with the help of its eigenfrequencies (eigenvalues) for two different types of ow geometries. First, a ow inside an enclosure with a rectangular cross-direction, through which the panel is travelling, is added to the equations of out-of-plane motion of the panel with the help of added mass coefficients. Secondly, a free stream potential ow obstructed by the travelling panel is analyzed using the analytical solution for the aerodynamic reaction pressure. Some numerical examples are given for both models.