During slug-flow conveying, particles are conveyed gently in the form of slugs partially filling the cross section of a pipeline. Unfortunately, this mode of flow is difficult to understand and to predict. In many theoretical studies, slugs are regarded as compact porous solid columns that are able to transfer axial stress into radial stress. A stress transmission coefficient calculated from theoretical models is then used to describe the stress states. Using a new measuring device that includes both stress and pressure sensors, horizontal single slugs were investigated to determine porosity and stress states within slugs of cohesionless granular material. Moreover, a special slug-catcher was developed to investigate the porosity profile over slug height. Independent of conveying velocity, slugs were found to be fluidized over their whole length and did not display any porosity gradient over the pipeline cross section. Nevertheless, high wall shear stress and normal stress were detected within each slug. The lowest stress values were detected at the pipeline top and the highest stress states at the pipeline side where particles move faster. The higher the supply air velocity, the higher the stresses induced by slugs. Since slugs are fluidized columns, bulk solids mechanics cannot be applied to explain the stress states occurring by slug flow. A new approach based on kinetic theory was proposed. First calculations involving a momentum exchange between particles and pipeline wall showed satisfying results.