The descent of a tread element of a tire rolling on a pavement on which a thin viscous fluid film is present is modeled. The tread element is assumed to be flat or curved and the pavement is assumed to possess a microtexture. Asymptotic results for the load supported by the tread element and the descent time are derived for different texture patterns. It is shown that the texture pattern as well as amplitude can significantly change the performance from that predicted by a smooth pavement assumption.