The initiation of a spark kernel and the subsequent propagation of a self-sustained flame in an internal combustion engine have been investigated numerically. A theoretical model which employs a two-dimensional cylindrical coordinate system and assumes axial symmetry has been developed. It considers the various physical and chemical phenomena associated with the ignition process and employs a detailed chemical reaction scheme for a methane-air mixture which contains 29 chemical species and 97 reaction steps. The thermodynamics and transport properties of the plasma at high temperatures are evaluated by a statistical thermodynamics approach, while assuming local thermodynamic equilibrium. Using the PHOENICS and the CHEMKIN codes, the appropriate conservation equations are solved in the domain of solution. It was concluded that the kernel growth can be described as a two-step process. In the early short stage (1-5 μs) the mass and energy transfer processes are very much dominated by the pressure wave and the violently expanding plasma kernel, while the contribution of the chemical reactions is negligible. This stage is followed by a much longer period in which diffusion and thermal conduction control mass and energy transfer as the flame becomes gradually self-sustained. Owing to the heat release by chemical reactions, the expansion of the combustible mixture is accelerated at the beginning of the diffusive stage.