In a flat knitting machine with knitting needles which have flexible shanksnd which are arranged in the needle channels of the needle beds, the flexible shanks of the knitting needles are each engaged from below in the region of an operating butt of the needle by a flexible shank of a Jacquard jack whose shank can be held either in an upper or in a lower position with respect to the needle bed. Selectively actuatable selection flaps are provided for selective extension of the Jacquard jacks into positions in which the needles can form stitches or tuck loops. In order to be able to withdraw the needles selectively to different withdrawn depths, the needles each have a further operating butt, additional withdrawal cam elements are provided on the knitting cam unit for engagement with the further operating butts, additional pressure cam elements are provided on the knitting cam unit in the region of the additional withdrawal cam elements to depress the first operating butts into the needle bed, and selectively actuatable selection flaps are provided for selective withdrawal of the Jacquard jacks into a position in which the first operating butts of the needles are not engageable by withdrawal cam elements.