The collapse of glass tubes, as used in the manufacture of optical fiber preforms, constitutes a problem involving Stokes flow, driven by surface tension and applied pressure. Undesirable, noncircular modes of deformation may grow or decay, depending on initial tube dimensions, radial viscosity variations, and the pressure differential across the tube wall. A two-dimensional model of the collapse process has been developed. Numerical results show trends that agree with experimental observations and are useful in the control of actual, three-dimensional collapse.