The tensile behaviour of semi-crystalline polymers, such as PP and PE, typically involves a necked region, of reduced cross-section, with neck "shoulders" that propagate throughout the length of the specimen. Soon after formation, the neck shoulders assume a constant shape and propagate with constant velocity. We have developed in-house image analysis software to automatically analyse the neck shape profile from image-sequences captured during tensile tests. In addition, we simultaneously measure the strain field, by tracking dots marked on the sample, and the force from the load cell of the tensile testing machine. The exact shape of the neck is governed by the strain rate sensitivity and strain hardening characteristics of the polymer, and so its underlying structure. Here we determine the steady-state neck profiles, formed in flat dog-bone specimens of various PP and PE grades, during tensile tests at elevated temperatures. We study how the neck shape depends on testing conditions (rate, temperature) and material characteristics (molecular weight and thermal history), and investigate the true stress/strain/strain-rate behaviour of the deformation. All these studies are complemented by Finite Element simulations of this necking process, which helps to enhance our understanding by elucidating the triaxial stress states induced. The Finite element predictions, in terms of draw stress and neck shape, agree very well with experiment. Also, we compare experimental and Finite Element results with simple analytical neck propagation models. Necking behaviour is of central importance in solid-phase deformation processes, such as die-drawing, which produces highly oriented polymer with extremely enhanced mechanical properties. Because this system determines both the necking and the stress/strain/strain-rate behaviour, it is very useful in predicting the performance of a polymer in deformation processing operations.