The invention relates to a system for automatic closure of sample vessels (PG), in particular of sample vessels (PG) with medical laboratory samples, with iii. a plurality of identically shaped, stackable closure caps (10) which have a convex outer face and a concave inner face and which are stacked in at least one closure cap stack in such a way that an upper closure cap (10) in the closure cap stack bears with its convex outer face on the concave inner face of a lower closure cap (10) lying immediately below in the closure cap stack, iv. a closure gripper (20) for gripping an uppermost closure cap (10) from the at least one closure cap stack, for transferring the gripped closure cap (10) to the sample vessel (PG) to be closed, and for introducing the gripped closure cap (10) into an opening of the sample vessel in order to tightly close the opening, wherein the closure gripper (20) has a centering piece which can be inserted into a closure cap (10) in such a way that it bears on the concave inner face of the closure cap (10). With such a system, automated closure of sample vessels is possible in a space-saving and efficient way. Furthermore, a method for automatic closure of sample vessels is also disclosed.