A theoretical model has been developed describing the propagation of a laminar, one-dimensional flame in a combustion chamber.The model aims specifically at illuminating the processes surrounding the flame propagation in the vicinity of the combustion chamber wall and the extinction of the flame (the quenching).The model assumes constant pressure for a two-reaction scheme with 6 chemical components (CnHm, O2, CO2, CO, H2O and N2). The equations describing the conservation of energy, mass, and species constitute a system of coupled parabolic differential equations, which are solved through a finite difference scheme with 9 grid-points. The boundary conditions specify the propagation or quenching situation. Temperature as well as concentration profiles through the flame are computed.Flame velocities and quenching distances are computed for a range of air-fuel ratios, physical constants and properties, both for methane and iso-octane. The comparisons between values of the quenching distances calculated with this model and experimentally determined values show acceptable agreement for air-fuel ratio above stoichiometric, but are somewhat low for air-fuel ratios below stoichiometric.