In order to accurately predict vehicle dynamic responses when traversing high obstacles or large bumps, appropriate tyre models need to be developed and characterised. Tyre models used in vehicle ride and durability are usually characterised by experimental tests on the tyre. However, limitations in rig design and operating conditions restrict the range of test conditions under which the tyre can be tested, hence characterisation of the tyre behaviour during extreme manoeuvres may not be possible using physical tests. In this study, a combination of experimental tests and finite-element (FE) modelling is used in deriving Flexible Ring Tire (FTire) Models appropriate for different levels of tyre/road interaction severity. It is shown that FE modelling can be used to accurately characterise the behaviour of a tyre where limitations in experimental facilities prevent tyre characterisation using the required level of input severity in physical tests. Multi-body simulation is used to demonstrate that the FTire model derived using extended range of obstacles produces more accurate transient dynamic response when traversing low and high road obstacles.