Simulation of upward solid-liquid flows in a vertical pipe was conducted. Trajectories of particles were obtained by means of the Lagrangian method with a collision model including inter-particle collisions and particle-wall collisions. Local mean velocities of the liquid phase were calculated numerically from the equations of continuity and motion by the SIMPLE scheme. The flow and collision were treated two-dimensionally. Three modes of calculation were conducted: non coupling, drag force coupling and coupling with both the drag force and the fraction of the fluid. The three calculations resulted in quite different concentration distributions. The effects of inter-particle collisions, particle properties, flow conditions and time intervals on concentration distributions of the particles were examined.