The tunnelling of electrons in resonant tunnelling diodes is studied within the framework of Bohm's interpretation of quantum mechanics. Bohm trajectories are studied in detail to determine whether they can be used for the Monte Carlo simulation of tunnelling devices. In agreement with the intuitive picture of the resonances, oscillatory Bohm trajectories are found, but only in some cases. The oscillatory behaviour is related to the relation between the transmission time and the local density of states in the quantum well of the device. Finally, we present the general guidelines for the implementation of a Monte Carlo simulator which uses Bohm trajectories to model quantum-mechanical tunnelling.