A set of essentially identical floor panels (1, 1') provided with a mechanical locking system comprising a flexible tongue, which is arranged in a displacement groove at a first edge of a first panel, and a tongue groove at a second edge of an adjacent second panel, the flexible tongue being configured to cooperate with the tongue groove for locking of the first edge and the second edge in a vertical direction, wherein the mechanical locking system further comprises a locking strip, at the first or the second edge, provided with a locking element configured to cooperate with a locking groove at the other of the first edge or the second edge for locking in a horizontal direction, wherein: the flexible tongue is displaceable in the horizontal direction in the displacement groove, an outer part of the flexible tongue comprises two or more curved tongue sections (Ts1, Ts2), each comprising a sliding surface, which is configured to cooperate with the second edge during locking, and a locking surface that is configured to lock against the tongue groove, the tongue sections (Ts1, Ts2) are spaced from each other in a length direction of the flexible tongue, the flexible tongue is curved in a locked and in an unlocked position, a first horizontal distance, from an outer upper edge of the first edge of the first panel to an outer edge of the flexible tongue, and a second horizontal distance, from the outer upper edge of the first edge of the first panel to an inner edge of the flexible tongue, varying along a length of the flexible tongue, the tongue sections (Ts1, Ts2) during locking are configured to be pressed inwardly by the second edge of the second panel such that the tongue sections are at least partially straightened and deformed, the tongue sections (Ts1, Ts2) are configured to move back towards their initial positions in a final stage of the locking such that said locking surface is inserted into the tongue groove, characterised in that the tongue sections (Ts1, Ts2) during locking are at least partially straightened and deformed to essentially straight rod shaped sections with a width that is essentially the same along essentially the entire length of the flexible tongue. the flexible tongue is displaceable in the horizontal direction in the displacement groove, an outer part of the flexible tongue comprises two or more curved tongue sections (Ts1, Ts2), each comprising a sliding surface, which is configured to cooperate with the second edge during locking, and a locking surface that is configured to lock against the tongue groove, the tongue sections (Ts1, Ts2) are spaced from each other in a length direction of the flexible tongue, the flexible tongue is curved in a locked and in an unlocked position, a first horizontal distance, from an outer upper edge of the first edge of the first panel to an outer edge of the flexible tongue, and a second horizontal distance, from the outer upper edge of the first edge of the first panel to an inner edge of the flexible tongue, varying along a length of the flexible tongue, the tongue sections (Ts1, Ts2) during locking are configured to be pressed inwardly by the second edge of the second panel such that the tongue sections are at least partially straightened and deformed, the tongue sections (Ts1, Ts2) are configured to move back towards their initial positions in a final stage of the locking such that said locking surface is inserted into the tongue groove,