The two-fluid theory has been used in order to model plug flow in a horizontal pneumatic conveying pipeline. A three-dimensional (3D) model, which enables simulation of dense phase flow, has been developed. The model solves the conservation equations for mass and momentum for the gas and solids phases by using a finite volume numerical method. Solids contact stress has been introduced and was described as a function of the bulk density. The numerical simulations demonstrated the formation and deformations of plugs along a horizontal pipe. Both axial and radial pressure drops have been examined and qualitatively compared with experimental data. It was concluded that due to plug creation and destruction, it is impossible to obtain the plug velocity by cross-correlation between various radial or axial pressure drops. The changes of the radial pressure drop is a very typical property of plug flow and as a result can be used to identify the transition from dilute phase flow to wave-like flow. This flow property can be used to examine the operational condition of pneumatic conveying systems.