Computational fluid dynamics simulations are used to investigate the pneumatic conveying of granular solids through an inclined pipe at different inclinations. Model predictions agreed reasonably well with the measurements reported by Tsuji and Morikawa in 1982 for mean gas and solids velocities. The results of influence of model parameters, inclination angle, and feeding conditions on the flow patterns were also reported. Particle-wall collisions were found to have a very significant effect on the solids distribution over the cross section of the conveying tube for large particles. Upon introducing finite-amplitude sinusoidal fluctuations in the gas velocity at the inlet of the pipe, solids density waves were observed to move along the conveying line with significant axial dispersions. (C) 2004 American Institute of Chemical Engineers.