A massive earthquake took place about 130 km of the coast of Japan 11 March 2012 and the subsequent tsunami caused severe damages to the Japanese infrastructure. During this event the Fukushima Daiichi Nuclear Power Plant (FD-NPP) had power failures that led to release of radioactive material into the atmosphere which was monitored at many places, especially in the northern hemisphere. We have used a stochastic random displacement particle model to simulate the radioactive dispersion. This was used to verify that the levels of radioactivity that were monitored can be modeled on the scale of the northern hemisphere. Xenon-133 (133Xe) is an inert gas that was released during the accident and Xenon may be considered as a passive tracer in the atmosphere. The 133Xe simulation shows good correlation with measurements from eight stations in the northern hemisphere both in magnitude and in temporal variations. This shows that the model can handle the dynamics well even though there in general is an estimation of the magnitudes. Measurements of particulate caesium-137 (137Cs) in Sweden and Taiwan have been used to verify the modelling of dispersion of particulate matter. 137Cs is assumed to attach to particles in the surrounding air when released from an NPP. Three different aerosol distributions have been tested to verify the importance of the aerosol spectrum. The study showed that the choice of different aerosol distributions was of minor importance compared to other effects, such as deposition schemes and dynamics on these scales, in the simulations. The magnitudes of the simulated 137Cs concentration after calibration of the model precipitation with the weather field precipitation showed good correlation with measurements. However, the variations in concentration were not as good described for particulate 137Cs as for 133Xe. Furthermore, the simulations show the importance of an accurate modeling of the wet and dry deposition. Major part of this work has been founded by the Swedish Radiation Authority, SSM.