Torsional motion of a truck driveline system is coupled with other motions of its components. In this paper, a comprehensive model of the truck driveline and body for vibration analysis was developed. Coupling of the torsional vibration of the truck driveline system with the body fore-aft and vertical vibrations was investigated. A mathematical model, including the torsional vibration of the driveline system and the whole body vibrations of the truck, was constructed. The driveline system was modelled as a set of inertia discs linked together by massless springs and the tyre was represented as having massless circumferential band which is elastically connected to the carcass with the bands being subject to longitudinal forces at the road surface. System behaviour at steady and transient runs was developed. Results were generated for the time history responses of the system due to engine fluctuating torque in steady running and due to friction torque induced by clutch during engagement in transient running. System response was investigated by integration of the system equation of motion using Runge-Kutta method and a computer program in FORTRAN was developed for this purpose. The system was found to be unstable in torsional and fore-aft motions for certain values of the system parameters due to self excitation force induced from the tyre/road contact and friction torque due to clutch engagement. The effect of several important design parameters on the system behaviour was investigated.