Off-road autonomous vehicles such as tractors and agricultural machinery require an important power traction to cope with mobility issues on soft soils and rough terrains. This paper presents a simplified version of tyre modeling as an adapted Burckhardt tire model based on an analytical Bekker-Wong wheel-soil interaction model. The Bekker-Wong model is a fractional model in space and takes into account the plasticity theory and soil mechanics, however such a model is too complex to be usable in real-time. An adapted version of the Burckhardt model helps having a more compact model that can be usable in real-time. In this paper, an adapted Burckhardt tire model has been optimized for the E-Tract simulator and experiments have been carried out to validate the tractor simulator.