We employed a new test technique to measure the tensile response of PMMA, Kevlar® and Dyneema® products at strain rates ranging from 10−4 to 323 s−1. We then extended this technique to allow quasi-static measurements at temperatures in the range −40 to 70 °C. We characterised a monolithic polymer blend, a Kevlar® 49 fibre yarn, a Dyneema SK75 yarn and a Dyneema® tape, exploring the effects of temperature and strain rate on their tensile responses. The sensitivities of the tensile properties to temperature and strain rate were correlated using the time-temperature equivalence, allowing estimates of the mechanical properties of Kevlar and Dyneema at strain rates in excess of 103 s−1.