The paper deals with numerical modelling of unsteady turbulent diffusive combustion in two chambers＇ containment wherein the fuel and oxidant are separated by a bulkhead with an orifice at the initial instant. Thus initial gradients of concentrations of species are present in the flow and the originating turbulence plays an important role not only in combustion but also in the process of mixture formation. The internal flows are modelled using the system of equations for unsteady multicomponent chemically reacting hows of compressible gaseous mixture. The k-epsilon model is used to determine turbulent characteristics of the flow: turbulent mass momentum and energy fluxes, distribution of kinetic energy for turbulent pulsations with account of its production and dissipation. The results of numerical modelling of turbulent combustion in cylindrical two-chambers vessel separated by a bulkhead with a coaxial orifice are presented depending on governing parameters of the problem. The dynamics of turbulent diffusion flame is investigated. The existence of an oscillating regime with several extinctions and reignitions is shown.