Numerous experimental investigations on the vertical transport of dense gas-solid suspensions indicate that particles tend to segregate toward the tube wall. Although models based on the kinetic theory analogy can predict such patterns for perfectly elastic particle-particle collisions, the predictive ability of these models breaks down for inelastic collisions. In the present effort, a mathematical model is developed that incorporates two mechanisms that give rise to the lateral segregation of solids : interactions associated with individual particles based on a kinetic theory treatment and interactions associated with collections of particles based on an analogy with single-phase turbulent flows. Although these two mechanisms have been treated independently by previous workers, their combined contributions to the overall flow behavior have not been thoroughly investigated. The effect of such a treatment on the sensitivity of the model predictions to the inelasticity of particle-particle collisions is explored. A key element in eliminating the undue sensitivity appears to be a consideration of the effects associated with the collective motion of particles on the kinetic theory expressions. The resulting model can predict the expected segregation patterns for systems characterized by inelastic collisions, as well as many of the other salient features of vertical gas - solid flows.