A method and an apparatus for an anticipatory thickness control in foil rolling by using characteristic lines stored in a process control computer of the individual manipulated variables (for example, strip tensions, rolling speeds) for various operating points (conditions of operation) or by using an on-line operating physical computing model, also in combination with a monitor control. The method includes the steps of determining the thickness deviations of the foil at the entry side of the roll stand and of compensating the thickness deviations by an anticipatory thickness control. The apparatus includes a thickness measuring device between the running-off reel and the rolling mill or the roll gap of the roll stand. The thickness measuring device is connected to a superordinated process control computer. Following the thickness measuring device is arranged a tensioning unit which serves to change the travel path of the foil strip between the running-off reel and the roll gap. For example, the tensioning unit elongates the travel path.