We investigate the effect of thermal expansion and gravity on the propagation of a triple flame in a horizontal channel with porous walls, where the fuel and oxidiser concentrations are prescribed. The triple flame therefore propagates in a direction perpendicular to the direction of gravity, a configuration that does not seem to have received any dedicated investigation in the literature. In particular, we examine the effect of the non-dimensional flame-front thickness epsilon on the propagation speed of the triple flame for different values of the thermal expansion coefficient alpha and the Rayleigh number Ra. When gravity is not accounted for (Ra = 0), and for small values of epsilon, the numerically calculated propagation speed is found to agree with predictions made in previous studies based on scaling laws [1] We show that the well known monotonic relationship between U and epsilon, which exists in the constant density case when the Lewis numbers are of order unity or larger, persists for triple flames undergoing thermal expansion. Under strong enough gravitational effects (Ra >> 1), however, the relationship is no longer found to be monotonic. For a fixed value of epsilon, the relationship between the Rayleigh number and the propagation speed is shown to vary qualitatively depending on the value of epsilon chosen, exhibiting hysteresis if epsilon is small enough and displaying local maxima, local minima or monotonic behaviour for other values of epsilon. All of the steady solutions presented in the paper have been found to be stable, except for those on the middle branches of the hysteresis curves. (C) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.