The capabilities of a sophisticated tire force and moment model are investigated under extremes in operating conditions. The “Magic Formula” is the example tire model used in this study. Parameter values and characteristic curves are determined by optimization for a passenger-car tire which was tested under high load and slip conditions. These values are then compared to estimated parameter values which would have been extrapolated for the high-load range had only less-extreme data been available.Longitudinal and lateral forces under simple-slip and steady-state conditions are studied. Calculations are performed using proven optimization software adapted for this particular purpose. Also investigated using the Magic Formula is lateral force arising from pure camber.The Magic Formula is able to model the tire characteristics well even at extremes in vertical load and slip. The results show that under parameter extrapolation, however, the longitudinal force characteristic degenerates even at modest slip ratio under high vertical loads. The lateral force characteristic does not follow the decrease in cornering stiffness experienced at high vertical loading when parameter values are extrapolated. The model is successfully used to model camber thrust even at high camber angles.