There have been many differing interpretations of plesiosaur neck posture and function (see figure below). I provide a break down of some of these interpretations in my blog article on elasmosaurid necks here. Indeed, the function of the long plesiosaur neck remains controversial and unresolved today (Martill et al. 1994). Despite this uncertainty, it likely provided a mechanism for approaching prey, such as schools of fish, with stealth and speed (Massare, 1988).
Contrary to early work (Zarnik, 1925, see figure below), the plesiosaur neck did not have the extreme flexibility required to coil up and strike prey in the manner of some snakes and pleurodiran turtles (Pough et al. 1996). Tall neural spines on the top of the neck vertebrae limited vertical (up and down) flexibility, while processes on the anterior and posterior surfaces of the vertebrae (prezygapophyses and postzygapophyses) limited horizontal (side to side) mobility. The neck was therefore relatively inflexible, so plesiosaurs could not adopt the swan-like pose often depicted in artwork of these creatures (Storrs, 1993).