Conservation of mass and momentum equations for the solid and for the gas phases was used to compute the hydrodynamics of flow of fluidized catalytic cracking particles in a vertical pipe (riser) for the 1995 benchmark modeling contest. The computer code predicted a new phenomenon: an off-center maximum flux. The computed time-average radial fluxes and particle concentrations agree with PSRI experimental data. The computer code also predicted the observed core-annular flow regime. For the lowest gas velocity and highest solids flux, the code predicted low-frequency, snakelike density oscillations.