It has been seen in physical experiments as early as the 1960’s that when a positively charged particle is injected into a crystal in certain directions and with sufficiently high energy, the particle can penetrate into the crystalline structure to a depth which is unexpectedly long. Such motions in the crystal are referred to as channelling trajectories. Herein, we consider a Hamiltonian model for particle motion in a crystal. We then proceed to show that the results of KAM theory are applicable to the model, and moreover that these result predict the existence of trajectories for the fired particle which do indeed penetrate the crystal deeply. Finally, we present the results of two series of numerical simulations which strongly suggest that this behaviour is observable in our model. / text