The invention relates to a medical device intended to be inserted into the lumen of a cavity of the human or animal body or in the lumen of a blood vessel. The invention is characterised in that said device comprises a probe (5) suitable for delivering a treatment by the endovenous route, and, at the terminal end thereof, a hooked flexible tip (1), wherein the angle α formed between the extension of the end portion of the probe (5) and the extension of the end portion of the tip (1) is strictly less than +90°, said tip comprising means (3) for delivering a treatment. The invention is particularly applicable to the treatment of varicose veins, reticular veins and spider veins.
