In this study, the steady 3D Stokes equations are used to analyse the slow viscous flow in such a tube whose deformation is described by geometrically non-linear shell theory. Finite Element methods are used to solve the large-displacement fluid-structure interaction problem. Typical wall deformations and flow fields in the strongly collapsed tube are shown. Extensive parameter studies illustrate the tube's flow-characteristics (e.g. volume flux as a function of the applied pressure drop through the tube) for boundary conditions corresponding to the four fundamental experimental setups. It is shown that lubrication theory provides an excellent approximation of the fluid traction while being computationally much less expensive than the solution of the full Stokes equations. Finally, the computational predictions for the flow-characteristics and the wall deformation are compared to the results obtained from an experiment.