An apparatus and a corresponding method for reading out a storage phosphor plate (2) with an insertion device for inserting a cassette (1) in which a movably disposed support (3) is located, on top of which the storage phosphor plate (2) lies, a read-out device (20) for reading out the storage phosphor plate (2) and a conveyance device (11, 12) which takes the storage phosphor plate (2) from the support (3) and conveys it in a first direction (R) to the read-out device (20). In order to achieve the most precise and reliable alignment possible of the storage phosphor plate (2) relative to the read-out device (20) in a simple way, a positioning device (13) is provided for shifting the support (3), on which the storage phosphor plate (2) lies, in a second direction (A) which is different from the first direction (R) so that the support (3) and the storage phosphor plate (2) are aligned relative to the read-out device (20).