[en] This is a report on the development of improved analytical methods for predicting puncture of radioactive material shipping containers. 59 static and dynamic puncture tests were conducted of lead-backed, uranium-backed, and unbacked flat, circular, stainless steel plates with several mild-steel punch configurations. It was found that analytical puncture prediction requires two essential elements: (1) a code that will accurately tract stress and displacement throughout the event and (2) a criterion for identifying when and if puncture occurs. (The puncture event is not self-evident from the calculations.) The NIKE2D finite element code was coupled with the puncture criteria -- a shear stress criterion for the lead-backed plates and a maximum effective plastic strain criterion for the uranium-backed plates; the results agreed very well with the test data