There is disclosed floor panels provided with a mechanical locking system for vertical and/or horizontal locking of a first edge (1) and a second edge (1') of adjacent floor panels comprising a plastic wear layer (3) and one or several plastic core layers (5a, 5b). One plastic core layer (5b) comprises several essentially vertical flexing grooves (19) with a vertical extension of at least about one third of a core thickness of the plastic core layer (5b).