Experimental data for the pressure-driven flow of concentrated lignocellulosic biomass (corn stover) in a circular pipe are presented. A positive curvature was observed in the pressure profile at steady state, both when the biomass was flowing, and for several minutes after the flow had stopped. After the flow into the pipe was stopped, biomass continued to be expelled for at least five minutes, suggesting that the material is compressible. Occasionally, the pressure and outlet flow rate exhibited rapid, transient fluctuations. The fluctuations would cease when dryer-than-average heterogeneities exited the pipe. A mathematical model is developed to treat the biomass as a compressible Bingham fluid with a density-dependent yield stress. This model quantitatively reproduces steady-state pressure profiles for both flowing and nonflowing states, and captures the transition between the two states after the inlet flow rate is set to zero. Our model cannot predict the rapid pressure fluctuations that appear to be associated with heterogeneities in composition. (C) 2018 The Society of Rheology.