This paper presents explicit finite element results for the transient macroscopic behaviour of a rolling automobile tyre. The aim of the research has been to develop the modelling methodology for an advanced LS-DYNA finite element simulation of a rolling tyre that can be used to provide internal transient stresses (and strains) to support the development of sensor systems technology. The methodology has been developed with an experimental 195 / 65 R15 tyre, which has provided physical test data to benchmark the performance of the numerical predictions for the free-rolling analysis on a rigid horizontal surface. Simulation results for a normal load of 3 kN and a speed of 20 km / h are presented to show the characteristics of stresses at the tyre / ground interface and, for the first time, internal stresses and strains at specific locations inside the tyre's structure. Such numerical results of the internal behaviour will be invaluable to tyre technologists who want to determine the optimal location for their sensor systems, and also to vehicle dynamists who want to establish the dynamic relationships between the contact patch stresses and the global tyre forces.