Abstract: A method for pumping away the oil in the aftermath of a blowout in an offshore oil well includes the steps of putting a support structure with a surrounding foil over the leaking oil well or pipe in order to create a hollow space overhead the leaking spot on the sea bottom. Thereafter, pumping water and oil through the top of the support structure for creating an underpressure below the foil, so the foil will be pressed onto the sea bottom due to hydrostatic pressure of the outside water. Then, continuously pumping away the liquid below the foil from within the support structure until it is pure crude oil and collecting the same. A related apparatus includes a support structure with an enclosure for providing a hollow room overhead a leaking spot or oil pipe and a reinforced foil having such size that it extends at least ten meters into the surrounding of the support structure. The reinforced foil is tightly attached to the lower edge of the enclosure of the support structure.