A mathematical model was developed to simulate sideways overturning of agricultural tractor-trailer systems. Sideways overturn of a tractor-trailer system was described by oscillatory motions of the tractor with respect to the first and second tipping axes, and of the trailer with respect to the drawbar hitch point when either the tractor or trailer rides over an obstacle on slopes. By a computer simulation, critical slope angles of the ground on which the tractor-trailer system is likely to sideways overturn were evaluated under the given operational conditions. Validity of the proposed mathematical model was proved by comparing the results of computer simulation and experiment with a model tractor-trailer system. A close agreement was observed between the two results.