Axisymmetric and non-axisymmetric gasless flames propagating in a narrow cylindrical sample of an energetic material are considered. The work is focused on the impact of radiative heat-losses from the outer surface of the slab on the flame structure and stability. A typical C-shaped response curve is found with two different flame velocities in the case of axisymmetric flames where the slowest velocity represents an unstable solution. Global linear stability analysis of such flames is performed. It is demonstrated that an increase in heat-losses promotes the flame instabilities for values of the Zel'dovich number lower than in the cases with the heat-losses neglected. The results of the stability analysis are successfully compared with the results of direct three-dimensional calculations showing oscillatory and spinning propagation of the gasless combustion waves. (C) 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.