The initiation and growth of necks in polymer tubes subjected to rapidly increasing internal pressure is analyzed numerically. Plane strain conditions are assumed to prevail in the axial direction. The polymer is characterized by a finite strain elastic–viscoplastic constitutive relation and the calculations are carried out using a dynamic finite element program. Numerical results for neck development are illustrated and discussed for tubes of various thicknesses. The sensitivity to the wave number of the thickness imperfections is studied with a focus on comparing a long wave length imperfection and a short wave length imperfection. After some thinning down at the necks, the mode of deformation switches to neck propagation along the circumference of the tube. A case is shown in which the necks have propagated along the entire tube wall, so that network locking in the polymer results in high stiffness against further expansion of the tube. The rate dependence of the necking behavior gives noticeable differences in neck development for slow loading versus fast loading.