In this paper we present the results of Monte Carlo simulations of positronium (Ps) swarm thermalization in helium (He) and water vapour. We have investigated the temporal evolution of energy and spatial parameters of the swarm and their sensitivity to the shape of the cross-section and the initial energy distribution. Positron anihilation spectroscopy (PAS) and positron emission tomography (PET) are techniques that depend on anihilation of positronium in materials and tissue. The results obtained point that the Monte Carlo technique shows good agreement with experimental results and is capable of accurately describing the behaviour of Ps particles including the energy, particle lifetime and the moment and location of the anihilation.