Pulsed field magnetisation (PFM) is the most practical method for magnetising bulk superconducting materials as trapped field magnets (TFMs), but the record trapped field achieved by PFM to date is still significantly less than the true trapped field capability of these materials. In this paper, a flexible numerical modelling technique based on the finite element method is used to provide a comprehensive and realistic picture of multi-pulse PFM, which has been shown to be effective in increasing the trapped field/flux over a single pulse. Firstly, the maximum trapped field capability of a representative sample is determined using two types of numerical model simulating field-cooling (FC) and zero-field-cooling (ZFC) magnetisation. Next, various sets of magnetic field pulses are applied to the bulk to analyse multi-pulse PFM. An increase in the trapped field can be achieved after a 2nd pulse and to do so an increased amplitude of applied field is required to maximize the trapped field fully. The numerical analysis shows that this occurs in subsequent pulses because it is more difficult for the magnetic flux to penetrate the sample and there is a lower temperature rise.