A systematic study of the diffusive-thermal instability of premixed tubular flames is carried out. The problem becomes amenable to a complete analysis in the frame of the diffusive-thermal approximation when a simplified flow field and the flame-sheet combustion model are used. The dispersion relation determining the growth rate of instability is obtained in an analytical form which therefore analyzed numerically. Stability diagrams showing stable and unstable states, in particular those manifesting the cellular flames, are presented. (C) 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.