A set of floor panels (1, 1') provided with a locking system comprising a separate flexible tongue integrated with an edge (4a, 4b) of a floor panel for connecting the edge vertically to an adjacent edge of a similar panel, wherein the flexible tongue has a length direction along the edge (4a, 4b), wherein the floor panels are provided with first and second connectors (9, 10, 6, 8, 14, 20, 31), the connectors are integrated with the floor panels and configured to connect adjacent edges, wherein the first connector comprises a locking strip with an upwardly directed locking element at an edge of a floor panel and a downwardly open locking groove at an adjacent edge of another floor panel for connecting the adjacent edges in a horizontal direction perpendicular to the adjacent edges, the second connector comprises the flexible tongue (10, 31) at an edge of a floor panel, and a horizontally open tongue groove (9, 20) in an adjacent edge of another floor panel for connecting the adjacent edges in vertical direction, the connectors being configured to be locked with angling or vertical motion, T characterised in that a least a part of the flexible tongue is configured to be displaced essentially horizontally and essentially in one direction only from an initial position to a final outer locked position, wherein the flexible tongue is configured to be twisted along the edge during locking, wherein the flexible tongue has a knee joint with a pressing extension extending essentially horizontally and a locking extension extending essentially vertically upwards with a locking part at an upper part above the knee joint, wherein the flexible tongue is configured such that pressing an adjacent edge of a panel vertically against the pressing extension causes the displacement of the locking part, wherein the locking part of the flexible tongue is arranged in an inner initial position in a displacement groove at an edge of a panel and that the locking part is configured to be displaced essentially horizontally and essentially in one direction only from the initial position to a final outer position in the tongue groove of another adjacent panel, wherein the flexible tongue is configured such that an angling along an edge triggers the displacement of the locking part at another edge, and wherein the flexible tongue comprises a reinforced plastic material. wherein the flexible tongue has a length direction along the edge (4a, 4b), wherein the floor panels are provided with first and second connectors (9, 10, 6, 8, 14, 20, 31), the connectors are integrated with the floor panels and configured to connect adjacent edges, wherein the first connector comprises a locking strip with an upwardly directed locking element at an edge of a floor panel and a downwardly open locking groove at an adjacent edge of another floor panel for connecting the adjacent edges in a horizontal direction perpendicular to the adjacent edges, the second connector comprises the flexible tongue (10, 31) at an edge of a floor panel, and a horizontally open tongue groove (9, 20) in an adjacent edge of another floor panel for connecting the adjacent edges in vertical direction, the connectors being configured to be locked with angling or vertical motion, T characterised in that a least a part of the flexible tongue is configured to be displaced essentially horizontally and essentially in one direction only from an initial position to a final outer locked position, wherein the flexible tongue is configured to be twisted along the edge during locking, wherein the flexible tongue has a knee joint with a pressing extension extending essentially horizontally and a locking extension extending essentially vertically upwards with a locking part at an upper part above the knee joint, wherein the flexible tongue is configured such that pressing an adjacent edge of a panel vertically against the pressing extension causes the displacement of the locking part, wherein the locking part of the flexible tongue is arranged in an inner initial position in a displacement groove at an edge of a panel and that the locking part is configured to be displaced essentially horizontally and essentially in one direction only from the initial position to a final outer position in the tongue groove of another adjacent panel, wherein the flexible tongue is configured such that an angling along an edge triggers the displacement of the locking part at another edge, and wherein the flexible tongue comprises a reinforced plastic material.