Starting with the kinetic theory for dilute solid/liquid two-phase flow, a mathematical model is established to predict the flow in a horizontal square pipe and the predictions are compared with LDV measurements. The present model predicts correctly two types of patterns of the vertical distribution of particle concentration observed in experiments, and also gives different patterns of the distribution of particle fluctuating energy. In the core region of the pipe, the predicted mean velocity of particles is smaller than that of liquid, but near the pipe bottom the reverse case occurs. In addition, full attention is paid to the mechanism for the vertical distribution of the average properties of particles such as concentration and mean velocity. From the kinetic-theory point of view, the cause of formation for different patterns of the vertical concentration distribution is not only related to the lift force exerted on a particle, but also related to the distribution of particle fluctuating energy.