Slug flow horizontal pneumatic conveying of granular materials is a complex phenomenon, involving many interacting properties. Investigating internal properties such as bulk density and bulk material stress, particularly via experiment, is limited by practical considerations. A combined 3D DEM + 2D CFD algorithm is introduced as a complementary means of investigating such properties. Important aspects of the simulation work include the extraction of bulk density, bulk material stress, stress transmission ratio and boundary stress data as functions of time and position in one and two dimensions. Such data is presented and analysed in the context of existing assumptions and a resulting one-dimensional model for bulk material stress within a slug.