Mathematical models were developed to predict the transitions between the different forms of transverse motion of free-flowing bed materials in rotating cylinders: sliding, surging, slumping, rolling, cascading, cataracting and centrifuging. Model calculations of the limits between these types of bed motion compare well with measurements of experimental rotating cylinders as well as published results from industrial practice. The motion behavior can be represented on a Bed Behavior Diagram that plots wall friction coefficient and Froude number against the filling degree. From this study, scaling criteria for the bed behavior were found to be the Froude number, filling degree, wall friction coefficient, ratio of particle to cylinder diameter, angle of internal friction, and static and dynamic angles of repose. The transition criteria worked out and the Bed Behavior Diagram provides the user of rotary kilns the possibility to estimate the type of motion of the bed materials used from measured particle characteristics. As a result, the bed behavior can be influenced through selection of operating variables such as rotational speed and filling degree or installation of lifting bars and flights.