A valve drive of an internal combustion engine, having a finger lever which acts at one end on a gas exchange valve and which is seated at the other end on a head of a housing of a support element, which housing runs in an axially movable manner in a reception bore of a cylinder head, the finger lever is acted on by a cam from the base circle from which there projects in a fixed manner an additional cam piece for generating an additional lift of the gas exchange valve, a bore extends from a bottom of the housing in the direction of the head, in the lower portion of which bore there runs a pressure piston which is axially movable relative to the housing and via the lower face of which the support element is mounted on a base of the reception bore of the cylinder head, a high-pressure chamber for hydraulic medium is formed between an upper face of the pressure piston and a ring part situated above said upper face and which is fixed with respect to the housing, and to generate the additional lift, the high-pressure chamber is flooded with hydraulic medium such that the housing is deployed relative to the pressure piston, supported on the hydraulic medium column accumulated in the high-pressure chamber, and to deactivate the additional stoke, the hydraulic medium in the high-pressure chamber is discharged such that the housing is retracted.