First principle is: NOT ALL PLESIOSAUR NECKS ARE THE SAME.
Plesiosaurs had all sorts of different necks of different anatomy, different lengths and different flexibility. That is the outcome when you have any sort of adaptive radiation. It is absurd to make blanket statements that all Plesiosaurs had necks that were alike even if some necks might have been longer than others or less flexible than others (To select only two variables)
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Plesiosaur-phylogeny-Benson-et-al-2012 |

The argument goes that Plesiosaurs had necks which they kept down in the water and could not hoist up into the air to form stretched-S or Periscope formations so commonly shown in the older reconstructions, like in this public-domain image example:
Actually going by the skeleton shown in this Russian illustration, I estimate that the vertebrae in the neck had enough wiggle room to assume any positions within the range as indicated, and that the body was substantial enough to be able to support the neck in these positions. (Brown is the original and the black lines are my extrapolations translating the estimates of the more liberal experts, The Russians I think would allow these parameters, I think. In American and European scientists it is the more conservative element that denies this degree of flexibility in Plesiosaurian necks.
Several Fossil finds had necks that could assume positions along these lines: some fossils are FOUND with their necks indicating a greater flexibility than some of the skeptics allow. Almost all of these are Plesiosaurs that had necks that were less than half the total length and substantial torsos.
Some Plesiosaur skeleton mounts continue to beerected and displayed as showing the traditional degree of Plesiosaur neck ability. If nothing else, this goes to show that not ALL experts go along with the idea that the necks could not be fitted into those patterns, and that this remains a matter of controversy. The following image is from
http://skywalker.cochise.edu/wellerr/fossil/reptile/plesiosaur4.htm
Below is a Canadian one. Several museum mounts indicate the neck falling naturally into a shallow S-curve in the vertical plane: the Canadian one shows this and so do many American ones.
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Elasmosaurus scale, also shows neck in shallow vertical S-curve |
In this case we also have a fossil showing the neck in a definitely snaky wiggle pose. Apart from the stomach being burst open in this specimen, most of the body was still mostly articulated:
From this fossil alone, t seems to me that Elasmosaur necks would have just about the flexibility indicated in this chart from a Scientific paper) which I have been criticized for running before:

However this is horizontal movement. The charge was also made that the vertebral spines on the Elasmosaur neck were too tall to allow for much vertical movement. let's check that part. Here is a replica of an Elasmosaur skeleton being built:
And here is a section of the neck. It looks to me as if there is plenty of free space all around to allow flexibility in all planes (all other possible factors excluded since we are only talking neural spines)
Now why should Scientists be insisting Elasmosaur necks were clumsy and could not be lifted out of the water? The answer it seems is more physics rather than anatomy.
THEIR NECKS WERE TOO DAMN LONG!
This ignores the possibility that the neck may be bent in the middle. However this is the practical reason why Elasmosaurs were stated to have necks which could not be held up out of the water. I have no problems with that.
We are not now and never have been talking in terms of the Elasmosaurs with extremely long necks!
All we have ever done (from Gosse on) is to suggest that we are dealing with a very large kind of Plesiosaur with a moderately long neck (less than twenty feet ): "Essentially a Plesiosaurus with the colossal magnitude of a Pliosaur" as Philip Gosse said in 1860
Romance of Natural History on Googlebooks
https://en.wikipedia.org/wiki/Plesiosaurus
https://en.wikipedia.org/wiki/Pliosaurus
https://en.wikipedia.org/wiki/Elasmosauridae
https://en.wikipedia.org/wiki/Elasmosaurus
https://en.wikipedia.org/wiki/Plesiosauria