The flame propagation in a solid composite energetic sample comprised of a solid energetic annulus surrounding a highly conductive core is investigated using one-step Arrhenius reaction mechanism. The steady-state solutions, its linear stability analysis and the results of direct numerical simulations of non-stationary problem are presented. It was found that the flame dynamics is highly subject to variation in the presence of the conductive core leading in some cases to a chaotic flame behavior or to stabilization of the flame propagation. It was demonstrated that for given combustion properties of the energetic material the kind of flame dynamics observed in the composite sample can be controlled by an appropriate choice of the experimental parameters such as the thickness of the fuel annulus deposited or the diameter of the heat conductive core. (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.