The thickness growth characteristics of flowing lava are investigated using a heat balance model and a two-dimensional model for flow of a Bingham plastic fluid down an inclined plane. It is found that yield strength plays a crucial role in the thickening of a lave flow of given flow rate. To illustrate this point, downstream thickness profiles and yield strength distributions were calculated for flows with mass flow rages of 104 and 105 kg/m-sec. Higher flow rates led to slow cooling rates which resulted in slow rate of increase of yield strength and thus greater flow lengths.