The origin of the rate-sensitive behaviour of plasticity over strain rate regimes from 10−5 to 105 s−1 has been assessed with reference to three key mechanisms: dislocation nucleation, time of flight (dislocation mobility) and thermally activated escape of pinned dislocations. A new mechanistic formalism for incorporating thermally activated dislocation escape into discrete dislocation plasticity modelling techniques is presented. It is shown that nucleation and dislocation mobility explain rate-sensitive behaviour for strain rates in the range 102 to 105 s−1, but cannot do so for significantly lower strain rates, for which thermally-activated dislocation escape becomes the predominant rate-controlling mechanism. At low strain rates, and for a model Ti alloy considered at 20 °C, the strong experimentally observed rate-sensitive behaviour manifested as stress relaxation and creep is shown to be captured well by the new thermal activation discrete dislocation plasticity model, which otherwise simply cannot be captured by nucleation or mobility arguments. Increasing activation energy leads to a higher energy barrier and as a consequence, a higher dislocation escape time. Conversely, increasing obstacle spacing tends to diminish the thermal activation time.