Background: Traumatic brachial artery injuries around the elbow, often associated with median and ulnar nerve injuries, are limb-threatening emergencies. Extensive collateral circulation may preserve distal pulses, masking significant vascular disruption and delaying diagnosis. Aim: To describe our institutional experience, emphasising diagnostic pitfalls, the role of computed tomography angiography (CTA) and multidisciplinary reconstruction in limb salvage. Methods: A retrospective review included four consecutive patients with traumatic brachial artery injury or suspected vascular compromise around the elbow treated at a tertiary trauma centre in Eastern India between January 2022 and December 2023. Clinical, radiological, operative, and outcome data were analysed. CTA assessed vascular integrity, and management involved plastic surgery, orthopaedics, and intensive care teams. Results: Four male patients (mean age 46.5 years; range 24–60 years) were included. Three injuries resulted from high-energy road traffic accidents and one from a glass laceration. CTA accurately identified vascular pathology in all imaged patients (n = 2). Two patients underwent autologous vein bypass grafting, while two required sural nerve grafting for median and/or ulnar nerve defects. Limb salvage was achieved in three patients (75%). One patient developed delayed arterial thrombosis despite an initially patent artery, resulting in irreversible limb ischaemia requiring above-elbow amputation. Conclusion: High clinical suspicion, early CTA, prompt revascularisation, and coordinated multidisciplinary management are essential for optimising limb salvage following complex brachial artery injuries. Relevance for patients: Early diagnosis and integrated specialist care can improve limb salvage and functional recovery, even in delayed presentations of complex upper-extremity trauma.