A three-dimensional finite element model of a rolling radial-ply truck tyre is developed to predict its vertical and cornering properties at relatively high speeds. The model includes a detailed representation of the tyre complex geometry and multi-layered composite structure including the carcass and belt plies, bead fillers and tread. LS-DYNA, a nonlinear finite element code, is used as the simulation tool. An algorithm is developed for efficient formulation of the model for parametric analyses. The validity of the proposed tyre model is demonstrated by comparing the predicted load-deflection, cornering and free vertical vibration characteristics with the reported experimental data. The simulation results revealed robust behaviour of the tyre model up to rolling speeds of 100 km/h. The verified tyre model is subsequently employed to study the influences of various operating parameters, namely, the inflation pressure, vertical load, rolling speed and road friction on the tyre vertical and cornering properties.