During the early stages of the plastic deformation of a polycrystal, dislocations can pile-up against grain boundaries. Experimental results on large-grained materials have provided excellent verification of this phenomenon. Such a pile-up may activate dislocation slip in the neighbouring grain. Whether this occurs depends on the misorientation between the grains and the resolved shear stresses in the affected grain. Several approximate criteria have been proposed to predict the occurrence of this mechanism. Here, the problem will be assessed directly by calculating the Peach-Köhler force produced by a single dislocation pile-up in one grain on all the possible slip systems in the neighbouring grain, in combination with the effect of the applied external stress as obtained through calculation of the Schmid factor. It will be seen that the problem is significantly more complex than what is generally assumed in basic explanations of the Hall-Petch effect: highly localised stress concentrations are generated for certain misorientations, which are capable of punching out small dislocation loops which may then propagate into the neighbouring grain.