Second-order moment method of particles is proposed on the basis of the kinetic theory of granular flow. Closure equations for the third-order velocity moments are presented to account for the increase of the probability of collisions of particles on the basis of the elementary kinetic theory and order of magnitude analysis. The boundary conditions for the set of equations describing flow of particles are proposed with the consideration of the momentum exchange by collisions between the wall and the particles. The distributions of velocity, concentration and moments of particles are predicted. Simulated results are compared with experimental data measured by Tartan and Gidaspow and Bhusarapu et al. in risers, and Tsuji et al. in a vertical pipe. The effects of the closure equations for the third-order velocity moments and the fluid-particle velocity correlation tensor on flow behavior of particles are analyzed. (C) 2012 American Institute of Chemical Engineers AIChE J, 2012