The unsteady motion at zero Reynolds number of a semi-infinite bubble advancing through a fluid-filled, flexible-walled channel, a model for the reopening of a collapsed lung airway, is described using asymptotic and numerical methods. The channel walls are supported by external springs and are held under large longitudinal tension, so that they are everywhere almost parallel although substantial transverse wall deflection is possible over long lengthscales. An asymptotic theory is developed by extracting, from existing numerical studies of bubble propagation in parallel-sided channels, key quantities associated with the two-dimensional Stokes flow in the neighbourhood of the bubble tip. These quantities enter boundary conditions for long-wavelength approximations of capillary numbers Ca (i.e. dimensionless bubble speeds), provided the wall tension is sufficiently large. Predictions of bubble pressure pb for steadily propagating bubbles, given (in some cases as explicit formulae) as a function of Ca, show good agreement with new and existing1 numerical simulations obtained by the boundary Element Method. The pb-Ca relation is non-monotonic:1 the asymptotic model provides a straightforward way of establishing the stability of the branch of solutions corresponding to motion in which the advancing bubble 'peels apart' the channel walls, for which pb increases with Ca. The model demonstrates that the dominant resistance to reopening arises from the very low induced pressures in the fluid ahead of the advancing bubble tip.