Abstract: A foundation for a mast, supporting pillar, rails, and the like, comprising an anchoring portion (2) of hollow section design open at the bottom and adapted to be driven into the ground by being vibrated, and a inner (3,3'), and, if desired, and outer (4) ground consolidating element. Preferably at least the inner ground consolidating element (3) is arranged for longitudinal displacement inside the anchoring portion (2) so that the earth entering from below into the interior of the anchoring portion (2) is consolidated during the entire period of sinking the anchoring portion (2) into the ground by vibrating it. In similar manner, also the outer ground consolidating element (4) may be arranged to be displaceable in longitudinal direction.A vibrator suspended from construction equipment or an airship and lowered from the same under loading which acts on the anchoring portion and corresponds approximately to the dead weight of the vibrator (about 1.5 to 3.