Typically a ‘smaller is strong’ size effect is seen when testing objects at the micro and nanoscales. This has significant consequences when using these tests to replicate and understand component level performance, for instance in materials discovery programmes. In this computational plasticity study, we follow the micro-cantilever experimental approach of Gong et al. for determination of size-dependent hcp crystal slip strengths and replicate size sensitivity using length scale dependent crystal plasticity modelling. A fundamental derivation of the back stress term required to harden slip systems according to the mechanism of dislocation pile up is introduced. Model micro-beam single crystals in Ti-6Al under four-point bending were examined which showed that the size-independent slip strength could be correctly determined but that the size-strengthening effect was under predicted. This was attributed to the averaging of discrete dislocation behaviour in to the continuum slip rule required within the crystal plasticity formulation