In this thesis, a numerical and theoretical investigation of the Pulsed Pressure Chemical Vapour Deposition (PP-CVD) progress is presented. This process is a novel method for the deposition of thin films of materials from either liquid or gaseous precursors. PP-CVD operates in an unsteady manner whereby timed pulsed of the precursor are injected into a continuously evacuated reactor volume. A non-dimensional parameter indicating the extent of continuum breakdown under strong temporal gradients is developed. Experimental measurements, supplemented by basic continuum simulations, reveal that spatio-temporal breakdown of the continuum condition occurs within the reactor volume. This means that the use of continuum equation based solvers for modelling the flow field is inappropriate. In this thesis, appropriate methods are developed for modelling unsteady non-continuum flows, centred on the particle-based Direct Simulation Monte Carlo (DSMC) method. As a first step, a basic particle tracking method and single processor DSMC code are used to investigate the physical mechanisms for the high precursor conversion efficiency and deposition uniformity observed in experimental reactors. This investigation reveals that at soon after the completion of the PP-CVD injection phase, the precursor particles have an approximately uniform distribution within the reactor volume. The particles then simply diffuse to the substrate during the pump-down phase, during which the rate of diffusion greatly exceeds the rate at which particles can be removed from the reactor. Higher precursor conversion efficiency was found to correlate with smaller size carrier gas molecules and moderate reactor peak pressure. An unsteady sampling routine for a general parallel DSMC method called PDSC, allowing the simulation of time-dependent flow problems in the near continuum range, is then developed in detail. Nearest neighbour collision routines are also implemented and verified for this code. A post-processing procedure called DSMC Rapid Ensemble Averaging Method (DREAM) is developed to improve the statistical scatter in the results while minimising both memory and simulation time. This method builds an ensemble average of repeated runs over small number of sampling intervals prior to the sampling point of interest by restarting the flow using either xi a Maxwellian distribution based on macroscopic properties for near equilibrium flows (DREAM-I) or output instantaneous particle data obtained by the original unsteady sampling of PDSC for strongly non-equilibrium flows (DREAM-II). The method is validated by simulating shock tube flow and the development of simple Couette flow. Unsteady PDSC is found to accurately predict the flow field in both cases with significantly reduced run-times over single processor code and DREAM greatly reduces the statistical scatter in the results while maintaining accurate particle velocity distributions. Verification simulations are conducted involving the interaction of shocks over wedges and a benchmark study against other DSMC code is conducted. The unsteady PDSC routines are then used to simulate the PP-CVD injection phase. These simulations reveal the complex flow phenomena present during this stage. The initial expansion is highly unsteady; however a quasi-steady jet structure forms within the reactor after this initial stage. The simulations give additional evidence that the collapse of the jet at the end of the injection phase results in an approximately uniform distribution of precursor throughout the reactor volume. Advanced modelling methods and the future work required for development of the PP-CVD method are then proposed. These methods will allow all configurations of reactor to be modelled while reducing the computational expense of the simulations.