The dense phase mode may be advantageous over the dilute phase mode, for some pneumatic conveying problems, because it causes less erosion of the pipeline, less attrition of the material, requires less dust collection and is effective even for smaller pipe diameters. The objective of this study is to numerically determine the parameters that govern the formation slugs in dense phase conveying. The distributed Lagrange multiplier/fictitious domain method (Glowinski et al. 1998 and Singh et al. 2000) is used to perform direct simulations of the motion of solid and gas phases in pipes with rectangular cross-sections. In this approach the exact governing equations are solved at scales finer than the particle size and no ad hoc two-phase flow model is used. Simulations are started by placing a particle slug in the flow. Several cases were simulated to understand the role of gravity, the particle density and the strength of applied pressure gradient in the formation and destruction of slugs. When the applied pressure gradient is increased the slugs become more compact, their velocity in the flow direction increases and they remain intact for longer time durations. A reduction in the pressure gradient, on the other hand, causes the particle velocity to decrease and consequently they sediment and simply roll on the bottom. The reduced gravity causes the slug to disintegrate and the center of mass of the slug moves upwards against gravity. The increased viscosity of the fluid, for a fixed pressure gradient, causes the particle to settle on the bottom of the channel under gravity.