Floor panels are provided with a mechanical locking system including a flexible locking element in a locking groove which during a horizontal motion is displaced vertically. A panel system including a plurality of rectangular panels with long and short edges which are mechanically connectable to each other along at least one pair of adjacent edges, said panels each being provided with a tongue and groove formed in one piece with the panels for mechanically locking together said adjacent edges at right angles to the principal plane of the panels, thereby forming a vertical mechanical connection between the panels, said panels being provided with a first locking element at one first edge formed in one piece with the panel and a locking groove at an opposite second edge, the locking groove being open towards a rear side or a front side of the panel.