Thoraco-brachial outlet syndrome is little known to the general public. However, it is a relatively common pathology, which generally corresponds to nerve compression in the neck and shoulder region. They would involve compression of the lower trunk of the brachial plexus sometimes of the subclavian vessels as these structures cross the thoracic outlet. The diagnosis is difficult, and gives rise to frequent medical errors and the methods have not been well established. Treatment includes physiotherapy, painkillers and, in the most complex cases, surgery due to mechanical stress. We report the case of a 39-year-old patient suffering from poorly systematized pain in the right upper limb associated with paresthesia and cramps and edema. The radiological assessment revealed a SDTB per supernumerary cervical rib with partial compression of the subclavian artery and vein. She benefited from a resection of the supernumerary rib and release of the crossing followed by physiotherapy. The surgical excision of this rib resulted in complete indolence the day after the operation, lasting one year later. The aim of this article is to present the surgical procedure for this pathology and the interest of which is to recall the physiopathology, the diagnostic means, the indications and the therapeutic strategy.