A bulk density increase due to degassing during emplacement may have a significant influence on the thickness of a lava flow and the rate at which it advances. We present a theoretical model of a lava flow that loses enough volatiles to cause density changes along the path of the flow. We assume that the flow is emplaced as a single, isolated unit and the bulk rheology (e.g., viscosity) is a function of distance from the vent. This type of model is applicable to solitary lobes of basaltic aa and isolated sheets of pahoehoe that advance as a fluid continuum with bulk lava density changes as a function of distance along the flow path. Equations for the flow thickness and the bulk density profiles are derived from mass and volume conservation. Formulas are tabulated for thickness and density profiles for various combinations of flow rates, rheologic changes, and degassing rate functions. We also tabulate formulas for estimating parameters associated with the form and rate of degassing from field data. The Mauna Loa 1984 1 flow is a typical example of a flow showing evidence of a bulk density increase and is used to estimate the model parameters. Thickness and density profiles are then computed for a range of plausible lava densities, two different rate functions for the loss of volatiles, and two different models of viscosity change. Results indicate that the thickness profile of a lava flow can be significantly affected when there is a large difference between the density at the vent and at the flow front. For relatively high rates of degassing, the flow profile has a maximum thickness located progressively closer to the vent as the rate of degassing increases. For depth-dependent degassing, an increase in viscosity acts to thicken the flow, which increases the rate of degassing, thus mitigating the thickening influence of the increasing viscosity. Degassing while a flow is active can increase the duration of emplacement by as much as 60%. We find that the flow thickness profiles are sensitive to the choice of flow rate and the initial density, regardless of the form of the degassing function. The nature of the flow rate can significantly affect the shape of the profile as well as the flow front thickness. When the rate of volatile loss depends on the flow thickness, the density profile depends explicitly on the way the rheology changes along the flow path. In all cases, density increases during emplacement counter the tendency of a flow to thicken due to increases in viscosity or resistance to flow with distance. Thus the parameters that define the rate of degassing, and the consequent density change along the path of a flow, emerge as important variables for a quantitative understanding of flow emplacement. ¿ 2001 American Geophysical Union