The behavior of solid inertia particles carried with significant slip velocity in turbulent gas-solid flow in a horizontal channel is investigated. Our mathematical analysis shows that, for such motion, particles have substantial transversal velocity and so they interact intensively with the walls when the Stokes number exceeds a threshold value. The mathematical description of such motion of particles is based on consideration of two particle flows moving towards each other from opposite walls and traversing through the center of the channel. The transport equations of particle mass and linear and angular momenta are integrated along the whole width of the channel. It was found that the Magnus lift force (in addition to the drag force) plays a significant role in the transversal motion of particles. The calculations on the motion of particles with various size in channels of different width for different velocities of the carrier flow show that the model presented does describe a two-phase flow with the slip velocity. Regardless of the fact that our experimental results were obtained for a pipe and the calculations, by contrast, were carried out for a flat channel, the numerical results for the velocity distribution of both phases, as well as that for the slip velocity, are in good agreement with experimental ones. Some discrepancy is found only for the description of particle mass concentration. Our model for a flat channel describes almost uniform distribution of particle mass concentration while our experiments, by contrast, show a gradient distribution fading towards the pipe wall. Apparently this results from the influence of the wall curvature of the pipe.