A modelling study of the ignition and explosion behaviour of quiescent methane/air mixtures caused by a radiatively heated inert particle has been carried out. Selecting the particle size much larger (about 2000 times) than the radiation wavelength reduces interference from Mie scattering. However, this results in axial non-symmetry of the processes of heat and mass transfer between, and within the particle and the surrounding gas phase. In order to simplify the model, the full number of space variables was reduced to one and a correlation factor between the cases of uniform and non-uniform radiative heating of the particle was established. The numerical simulations are compared with experimental results from previous studies. The theoretical predictions correlate well with the experimental values if the correlation factor is taken into account, however the absence of such a factor leads to significantly higher values (about 10 times) of the critical radiation power flux.