Analysis of lean premixed freely propagating flames in narrow adiabatic channels of circular cross-section subject to a Poiseuille flow is carried out systematically within the context of a diffusive-thermal model. It is found that for flames with sufficiently low Lewis number multiplicity of solutions exists, in particular it is shown that for a given flow rate up to three different axisymmetric flames can coexist. The rest of the study is focused on the influence of the Lewis number and the channel radius on the flame stability, linking first the results to the stability properties of corresponding planar flame fronts. The global stability analysis, giving accurate threshold values of instability, shows that for flames with Lewis number lower than one non-axisymmetric monotonous perturbations can grow, while for flames with Lewis number larger than one unstable axisymmetric and non-axisymmetric oscillatory modes can appear. An increase in the flow rate leads to a loss of stability of axisymmetric flames for Le < 1 while for flames with Le > 1 the Poiseuille flow produces a stabilization effect. This analysis seems to have received no attention in the literature for flames in circular channels. Finally, the stability results are compared successfully with three-dimensional unsteady numerical simulations. They show that for Le < 1 non-axisymmetric flames propagating with a constant velocity appear for positive values of the flow rate. For flames with Le > 1, depending on the channel width, pulsating axisymmetric and rotating non-axisymmetric flames arise. It is demonstrated that when the non-axisymmetric oscillatory perturbations are the most unstable, the flame adopts a multi-headed non-axisymmetric shape and can propagate in a rotating manner while the central part of the flame advances at a constant velocity. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.