A multiphase particle-in-cell (MP-PIC) method has been developed. This numerical technique draws upon the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The MP-PIC method uses an accurate mapping from Lagrangian particles to and from a computational grid. While on the grid, continuum derivative terms that treat the particle phase as a fluid are readily evaluated and then mapped back to individual particles. The result of this procedure is a computational technique for multiphase Rows that can handle particulate loading ranging from dense to dilute, a distribution of particle sizes and a range of particle materials. The dense particulate model represents separated flows of particles and includes drag exerted by a gas phase, inter-particle stresses, particle viscous stresses and gas pressure gradients. Six problems are presented to demonstrate the MP-PIC method. This MP-PIC method has important applications in fluidized beds (combustion, catalytic cracking), sedimentation, separation and many other granular flows.