The numerical procedure of combustion modelling by the boundary–domain integral method (BDIM) is presented, based on detailed chemical and physical processes of the premixed gaseous fuel. The boundary element method is employed to solve the conservation equations of overall mass, momentum, energy and mass species. The law of mass action is applied to determine the chemical reaction rates representing the basis of the source terms in the conservation equations for mass species. A freely propagating flame including the forced ignition of a homogenous hydrogen–air mixture is calculated as an example problem of the numerical simulation of the combustion processes.