This study developed a theoretical approach to understanding how a set amount of a granular bed is discharged from a tilted rotary kiln (an empty cylinder) once its particle size distribution (PSD) is known and slumping motion occurs. The basis of the study is that the preparation of material for thermal treatment inside a rotary kiln (pyrolysis, gasification, and/or combustion) involves shredding to a desired particle size. Further mechanical stress results from the feeder screws moving material from storage toward the reactor. The most common PSDs found in uniform size reduction processes and mechanical stresses are Gaussian, log-normal, and Rosin-Rammler, of which the latter best fits the PSD in our study. Different particle diameters in the distribution result in an axial segregation when a slumping motion occurs, resulting in particles of different diameters leaving the kiln at different instants. After developing the model, the theoretical data showed good agreement when compared with experimental results obtained from downloading previously shredded carbonaceous material from a rotary kiln at 2 and 4 rpm rotational speeds. The mean residence times at steady state were determined for both rotational speeds and showed good agreement with data provided in the literature. © 2015 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.