Slug flow pneumatic conveying is a full-bore mode of flow within the dense-phase flow regime where bulk materials are transported in the form of slugs at conveying speeds below saltation velocity. The mechanism of slug-flow pneumatic conveying consists of particles being picked up from the stationary bed in front of a moving slug while the same amount of material is deposited behind the slug. Stress field modeling of the material slug is the first step in developing a prediction model for the pressure drop along a pneumatic conveying line. However, a reliable prediction strongly relies on an accurate assessment of several factors, including the particle properties, pipeline dimensions, and operating conditions. So far, the particle diameter has always been one of the crucial parameters, which is not desirable in regards to the limitations it imposes on the choice of bulk materials. This article focuses on one parameter, the stress transmission coefficient k(w), which relates the lateral wall stress within a slug of material to the axial stress. To date, this parameter could not be measured directly in an aerated material bed and had to be estimated. Inaccuracies within the prediction were therefore unavoidable. A newly designed test chamber now enables the measurement of the lateral and axial stresses within a slug, which leads directly to this stress transmission coefficient. This article outlines the design of the test apparatus and reports on the experimental results. For the two materials tested, an exponential correlation between the pressure on top of the slug (frontal stress) and the stress transmission coefficient was obtained. Calculating the wall friction coefficient leads to a constant value above a certain material-specific air velocity.