A mechanical connection connects panels edge sides to one another. Adjacent first and second panels can be locked in the horizontal and vertical direction by a substantially perpendicular joining movement. For vertical locking, a locking edge is arranged on the first panel and a locking element that can be displaced relative to the panels is arranged on the second panel. The locking element can be displaced behind the locking edge by a pivoting movement. A locking projection for displacing behind the locking edge and an arcuate guide arm guided in a guide groove of the second panel are designed to be partially withdrawn from the guide groove with a rotary or pivoting movement of the locking element by a leg. The leg projects from the guide groove of the locking element coming into contact with the first panel when being set down in a region below the locking edge.