Drawing of the hollow all-polymer Bragg fibers based on PMMA/PS and PVDF/PC materials combinations are demonstrated. Hole collapse during drawing effects the uniformity of a photonic crystal reflector in the resultant fiber. We first investigate how the core collapse effects fiber transmission properties. We then present modelling of fluid dynamics of hollow multilayer polymer fiber drawing. Particularly, hole collapse during drawing and layer thickness non-uniformity are investigated as a function of draw temperature, draw ratio, feeding speed, core pressurization and mismatch of material properties in a multilayer. Both the newtonian and non-newtonian cases are considered assuming slender geometries.