Pneumatic conveying plug flow, experiments have been carried through for horizontal flow, of cohesive silica and kaolin powders over a range of gas superficial velocities and plug lengths. The plug pressure drops and velocities were measured. It is observed that the pressure drop increases linearly with plug length and increases non-linearly with increasing gas superficial velocity. A two-layer model is developed to predict the dynamic behavior of the plug. The inner core of the plug is treated as a Coulomb solid and the shear region of the plug is treated as a frictional fluid. The powder rheology is an important input to the model. The powder rheology for cohesive and non-cohesive powders are measured and compared. The predicted pressure drops using the two-layer model agree well with those measured. As opposed to analyses that treat the entire plug as a Coulomb solid, the two-layer model correctly predicts the dependence of pressure drop on the gas superficial velocity. An inherent advantage of the current approach is that the dimensionless variables that govern dynamically similar plug flow are clearly identified in the solution.