Brachial plexus (BP) birth injury has a reported incidence of 1 to 4 per 1000 live births. During complicated deliveries, neonatal, maternal, and other birth-related factors can cause over-stretching or avulsion of the neonatal brachial plexus leading to injury. Understanding biomechanical responses of the neonate brachial plexus when subjected to stretch can offer insight into the injury outcomes while guiding the development of preventative maneuvers that can help reduce the occurrence of neonatal brachial plexus injuries. This review article aims to offer a comprehensive overview of existing literature reporting biomechanical responses of the brachial plexus, in both adults and neonates, when subjected to stretch. Despite the discrepancies in the reported biomechanical properties of the brachial plexus, available studies confirm the loading rate and loading direction dependency of the brachial plexus tissue. Future studies, possibly in vivo, that utilize clinically relevant neonatal large animal models can provide translational failure values of the biomechanical parameters for the neonatal brachial plexus when subjected to stretch.