A locking device comprises a key (10) and a locking cylinder (30). The locking cylinder (30) in turn is composed of a stationary cylinder housing (31) and a cylinder core (32) rotatably supported therein. In order to increase the break-in safety, it is proposed to use two types of plate closures (40, 50) in the cylinder core (32), the displacement of that closure pointing into two radial directions (41, 51) that differ from each other. The key (10) comprises planar outer surfaces (12, 13) disposed at an angle to each other, the two types of plate closures (40, 50) being parallel displaceable to said surfaces. Each of the two adjoining outer surfaces (12, 13) has a dedicated linear control path (21, 22), which varies in adjoining key sections transversely to the key longitudinal direction (29) for coding the key (10). Accordingly, the plate closures (40, 50) have a pair of mating sampling sites (42, 52), which are disposed in defined positions and interact with the associated control path (21, 22) when the key (10) is inserted and generate a mating coding analogous thereto in the locking cylinder (30). Each of the two types of plate closures (40, 50) engages on the dedicated control path (21, 22) thereof.