The impact of non-shearable particles on the stress required to propagate a twin is examined using numerical and analytical techniques. Of particular note is the nature of this effect in magnesium alloys where twinning can count for a significant fraction of the plastic strain. Dislocation Dynamics simulations are employed to calculate the Orowan bypass stress. It is seen that the stress for bypass can exceed that for a single twinning dislocation but under some circumstances it may be similar. The conditions that give rise to different regimes of behaviour are mentioned and the significance for magnesium alloy design is described.