A new theoretical framework for interpreting the cross-sectional geometry of self-formed lava channels is introduced. The method may be applied to any lava channel, or tube, and is demonstrated by studying thermal erosion by a hot, turbulently flowing lava. The cross section of a thermal erosion channel is often characterized by undercutting of the channel walls when the upper surface of the lava flow falls beneath the original ground level. The degree of lateral undercutting is shown here to be a function of the flow parameters, which enables the shape of the channel cross section to be used to determine a lower bound upon the lava flow rate. The solution for the geometry of the lava channel is then coupled to an existing two-dimensional model for thermal erosion by komatiite flows to determine the effects of lateral erosion and variable flow cross section upon cooling of the lava and contamination of the lava by assimilated ground material. Lateral thermal erosion is shown to lead to a thinning of the lava flow with time, even at a constant eruption rate, which reduces its erosive power and enhances cooling of the lava. Finally, a linear stability analysis of the evolution equation for the channel cross section suggests that inefficient lateral mixing in a thin lava flow can lead to a morphological instability and eventual splitting of the channel. The instability is suppressed at short wavelengths by the variation in melting rate with local wall curvature, and the fastest growing symmetric mode has a wavelength equal to half the channel width, which corresponds to the formation of midstream islands. ¿ American Geophysical Union 1995