This paper is concerned with the problem of viscous flow in an elastic tube. Elastic tubes collapse (buckle non-axisymmetrically) when the transmural pressure (internal minus external pressure) falls below a critical value. The tube's large deformation during the buckling leads to a strong interaction between the fluid and solid mechanics.

In this study, the steady three-dimensional Stokes equations are used to analyse the slow viscous flow in such a tube whose deformation is described by geometrically nonlinear 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.