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Plastic deformation of olivine at relatively low temperatures (i.e., low‐temperature plasticity) likely controls the strength of the lithospheric mantle in a variety of geodynamic contexts. Unfortunately, laboratory estimates of the strength of olivine deforming by low‐temperature plasticity vary considerably from study to study, limiting confidence in extrapolation to geological conditions. Here we present the results of deformation experiments on olivine single crystals and aggregates conducted in a deformation‐DIA at confining pressures of 5 to 9 GPa and temperatures of 298 to 1473 K. These results demonstrate that, under conditions in which low‐temperature plasticity is the dominant deformation mechanism, fine‐grained samples are stronger at yield than coarse‐grained samples, and the yield stress decreases with increasing temperature. All samples exhibited significant strain hardening until an approximately constant flow stress was reached. The magnitude of the increase in stress from the yield stress to the flow stress was independent of grain size and temperature. Cyclical loading experiments revealed a Bauschinger effect, wherein the initial yield strength is higher than the yield strength during subsequent cycles. Both strain hardening and the Bauschinger effect are interpreted to result from the development of back stresses associated with long‐range dislocation interactions. We calibrated a constitutive model based on these observations, and extrapolation of the model to geological conditions predicts that the strength of the lithosphere at yield is low compared to previous experimental predictions but increases significantly with increasing strain. Our results resolve apparent discrepancies in recent observational estimates of the strength of the oceanic lithosphere.