Step 1: Volkmann's ischaemic contracture is the end stage of untreated forearm compartment ischaemia, leaving a clawed hand with flexed wrist and fingers; the typical trigger is a supracondylar humeral fracture in a child.
Step 2: The vascular event centres on the brachial artery as it crosses the elbow. Damage or kinking there starves the flexor muscle bellies of blood. The resulting oedema and bleeding swell the compartment, the pressure rises, blood flow falls further, and a self-perpetuating compartment syndrome sets in that scars the muscle into a fixed deformity.
Step 3: The radial and ulnar arteries are continuations distal to the elbow, and the interosseous arteries are deeper branches; none of these is the principal site of injury in the textbook presentation, which is the brachial trunk at the elbow.
Step 4: The artery whose compromise produces this contracture is the brachial artery.
\[\boxed{\text{Brachial artery}}\]