Longitudinal thickness profiles are simulated for lava flows on Mars erupted under conditions identical to those of Episodes 2 and 18 of the Pu'u O'o eruption at Kilauea volcano, Hawaii. Three separate approaches are used to estimate the change in the Newtonian viscosity along the length of these flows. The first approach assumes that all parts of the flow are in uniform motion and the volumetric flow rate is conserved at all stations along the flow path. The second approach assumes the same Newtonian flow model but takes advantage of independently acquired advance rate data. The third approach uses a recent model for the conservation of lava volume. This model apportions the flow rate into an active, advancing component and a separate component that is stationary (e.g., levees, stagnant zones, stationary margins). Viscosity changes for all three approaches are compared, with new insights into the rheologic changes in the Pu'u O'o flows. The three approaches to flow emplacement are used as a basis for scaling the terrestrial flow thickness profiles to account for the difference in Mars gravity. For the same volumetric effusion rate and identical topography, explicit scaling for the lower gravity affects the initial flow thickness and advance rate. More subtle is the implicit influence of the lower gravity on the viscosity change along the flow path. Differences in viscosity change estimated by all three models are magnified when applied to lava flows on Mars. To illustrate the sensitivity of relative viscosity estimates on the assumed flow rate model, we also estimate viscosity increases for lava flows at Ascraeus Mons, Elysium Planitia, and Alba Patera. We show that the third model consistently predicts significantly greater increases in viscosity and must be considered when analyzing channelized flows where significant volumes of material have been lost to stagnant margins during emplacement. ¿ 1998 American Geophysical Union