We have used new compositional information on Martian basaltic rocks from the Mars Exploration Rover Spirit and data from new stereo imaging by the High Resolution Stereo Camera (HRSC) on the Mars Express orbiter to constrain an existing analytical-numerical computer model to assess the potential of Martian lavas to form lava channels by erosion of substrate. The basaltic rocks studied in Gusev crater by Spirit have compositions consistent with lavas of higher liquidus temperature and lower dynamic viscosity than terrestrial tholeiitic basalts, suggesting that they had a greater potential for turbulent flow and erosion of substrate during flow emplacement than terrestrial basalts, more similar to lunar mare basalts. We modeled a specific case to determine whether these lavas could have formed part of a >66 km long channel on the Martian shield volcano Hecates Tholus. This channel formed on relatively steep slopes (~2--8¿), based on measurements from the HRSC Digital Terrain Model. Our results suggest that erosion rates were of the order of tens to hundreds of centimeters/day, depending on flow rate and ice content of the substrate. Eruption durations required to erode the Hecates channel (~100--30 m deep over the first ~20 km, depth decreasing downstream) range from weeks to months, which are consistent with the known eruption durations of terrestrial basaltic lavas and the previous modeling of Wilson and Mouginis-Mark (2004). Any Hecates lava channels formed from erosion by lava could have served as conduits for later fluvial activity, as recently described by Fassett and Head (2004, 2005).