A dynamic tire friction model based on the LuGre friction model has been developed recently. The model includes the longitudinal and lateral forces, as well as the self aligning torque. It has originally been derived in the distibuted form, and transformed to the simpler lumped form with only three internal states. The lumped model has been based on the simple uniform normal pressure distribution. It is extended in this paper for the more realistic case of a non-uniform normal pressure distribution, in order to provide a consistent prediction of the self aligning torque static curves.