Pressure drop in a radial flow reactor occurs when process flow crosses the packed catalyst bed installed between the two concentric perforated screens during operation. This pressure drop generates the lateral bed stress against the reactor’s perforated screens to shift. The pressure drop will further grow as catalyst attrition increases in production. For an outward radial flow, the pressure drop may exert higher stresses to the outer screen as the packed bed is pushed toward it. An extreme case is when the entire catalyst bed could be pinned to the outer screen of the reactor by enough pressure drop. This could cause the internal components to be overly stressed on the excessive bed load, for which the components might not have been designed adequately. Predicting how radial pressure drop impacts the bed stress and shifts the load distribution is important in preventing mechanical failure during operation. In this study, an analytical model is derived based on Janssen’s theory, a classical semi-empirical granular solid material model, to examine a generic packed catalyst bed in an outward radical flow reactor. A modification to Janssen’s theory is introduced to include pressure drop in order to explore its effects on bed stress and load. The critical condition is derived.