Pneumatic conveying is an important technology for industries to transport bulk materials from one location to another. Different flow regimes have been observed in such transportation processes, but the underlying fundamentals are not clear. This article presents a three-dimensional (3-D) numerical study of horizontal pneumatic conveying by a combined approach of discrete element model for particles and computational fluid dynamics for gas. This particle scale, micromechanic approach is verified by comparing the calculated and measured results in terms of particle flow pattern and gas pressure drop. It is shown that flow regimes usually encountered in horizontal pneumatic conveying, including slug flow, stratified flow, dispersed flow and transition flow between slug flow and stratified flow, and the corresponding phase diagram can be reproduced. The forces governing the behavior of particles, such as the particle-particle, particle-fluid and particle-wall forces, are then analyzed in detail. It is shown that the roles of these forces vary with flow regimes. A general phase diagram in terms of these forces is proposed to describe the flow regimes in horizontal pneumatic conveying.