A flooring system comprising a plurality of rectangular floor panels with short edges (1, 1') and long edges (2, 2', 2"), wherein the panels are adapted to be installed on a sub floor and connected to each other with a long edge mechanical locking system for locking the panels vertically and horizontally, said locking system comprising a tongue (10, 30) and a tongue groove (9, 20) for mechanically locking together adjacent edges vertical to the horizontal plane, forming a vertical mechanical connection between the panels, and a locking element at a first long edge and a locking groove at an opposite second long edge thereby forming a first horizontal mechanical connection between adjacent long edges (2, 2') locking the panels to each other in a direction parallel to the horizontal plane and at right angles to said adjacent long edges, wherein the panels are provided with a short edge locking connection comprising a separate tongue, for locking adjacent short edges (1, 1') in a first vertical direction, inserted in a fixation groove at a short edge(1, 1') of a panel, wherein the separate tongue is at least partly flexible and/or displaceable, and a locking strip and a locking cavity for locking adjacent short edges (1, 1') in a second vertical direction, wherein the long edges are provided with a second horizontal mechanical connection locking the panels to each other along said adjacent long edges, in a direction parallel to the horizontal plane and parallel to said adjacent long edges, when the panel are laying flat on the sub floor, characterised in that the short edge locking connection is configured to lock the adjacent edges in the vertical directions only, said second horizontal mechanical connection comprises a flexible and compressible material (16, 16a, 16b) which is applied in an upper part of said locking groove as a layer, and wherein an upper part of said locking element is formed such that two horizontally opposite edges of said locking element press against said flexible and compressible material (16, 16a, 16b). the panels are adapted to be installed on a sub floor and connected to each other with a long edge mechanical locking system for locking the panels vertically and horizontally, said locking system comprising a tongue (10, 30) and a tongue groove (9, 20) for mechanically locking together adjacent edges vertical to the horizontal plane, forming a vertical mechanical connection between the panels, and a locking element at a first long edge and a locking groove at an opposite second long edge thereby forming a first horizontal mechanical connection between adjacent long edges (2, 2') locking the panels to each other in a direction parallel to the horizontal plane and at right angles to said adjacent long edges, wherein the panels are provided with a short edge locking connection comprising a separate tongue, for locking adjacent short edges (1, 1') in a first vertical direction, inserted in a fixation groove at a short edge(1, 1') of a panel, wherein the separate tongue is at least partly flexible and/or displaceable, and a locking strip and a locking cavity for locking adjacent short edges (1, 1') in a second vertical direction, wherein the long edges are provided with a second horizontal mechanical connection locking the panels to each other along said adjacent long edges, in a direction parallel to the horizontal plane and parallel to said adjacent long edges, when the panel are laying flat on the sub floor, characterised in that the short edge locking connection is configured to lock the adjacent edges in the vertical directions only, said second horizontal mechanical connection comprises a flexible and compressible material (16, 16a, 16b) which is applied in an upper part of said locking groove as a layer, and wherein an upper part of said locking element is formed such that two horizontally opposite edges of said locking element press against said flexible and compressible material (16, 16a, 16b).