An apparatus for tying together a bundle of cut flowers with an elongate elastic tying material comprises a tying unit intended for pulling in and tying an amount of the elongate elastic tying material around said bundle, a storage unit for holding a reel having wound thereon a stock of said elongate elastic tying material and a guiding assembly intended for guiding the elongate elastic tying material from the storage unit towards the tying unit. The storage unit defines a central shaft for receiving thereon the reel, which is oriented such that the guiding assembly is capable of unwinding and removing the elongate elastic tying material from the reel in a removal direction substantially in parallel to said central shaft. The storage unit is provided with a restraining member intended for, with a restraining force, engaging at least a forward circumferential rim, as considered in said removal direction, of the stock of said elongate elastic tying material wound on the reel.
