Few studies have actively approached the premise of sauropod neck position from a purely biomechanical viewpoint. Those that do, however, tend to differ on their results. This is generally due to 1) taxon sampling, 2) methods used, or 3) how much of the biomechanical data was used in the conclusions phase of the work.
As a short summary, data has been taken from the ability to calculate blood-pressure in sauropods, ecological feeding envelopes, and the apparent ability to predict the neck posture, almost exclusively as a beam-like structure. A new short paper by DFG Research Unit 533′s Andreas Christian  helps add to the debate by pulling two of these data points into one model, that of the energy required to raise the head versus moving about, and that of the intervertebral stresses on the individual cervical vertebrae involved in the head-lift exercise. While Christian only involved one taxon (Euhelopus zdanskyi ), he had previously worked on another, Brachiosaurus brancai , solely concerning the biomechanical model of the neck position.
Few papers have directly involved the position of the neck in sauropods scientifically (rather than anecdotally) due to the problems of puny mortal men moving gigantic fossilized vertebrae (most sauropods are fairly large, regardless of the original lighter weight of the bones while the animal was alive). This paper addresses the issue of the energy related to raising the head a few meters relative to walking 100 more meters. Presumably, if food were evenly distributed along the group but also up in trees, a sauropod should prefer the least expensive route for attaining more food. Thus, this paper argues the principle others have, in reducing a sauropods journey to raising the head.
If this were all the paper did, however, it wouldn’t be much of one, and parroting untestable assumptions about habitat distribution of foods. Christian also addresses the stresses at various postures at each intervertebral joint, and reasons from the data that the base of the neck was the point of primary movement, supplemented by movement neat the base of the skull (where individual selectionary preferences would occur); much of the rest of the neck would remain stationary. According to the data, mere inclination of the neck relieves stress along the neck, and as noted in the figure, stresses are focused towards the base of the neck.
Hypothetical neck positions have been surmised from various purposes, but rarely tested directly. Assessing the natural stresses on the intervertebral joints helps explain something we know, however: a cantilevered beam resists more external stresses when inclined. The actual mechanical properties are nice to follow up studies like this, including why sauropods vary in cervical rib morphology, neural spine anatomy, etc. These features dominate sauropod cervical description, and many characters are gleaned from them for phylogenetic analysis. While a beam-like structure with little mobility between most of the elements could be expected in an animal whose sole purpose for having a long neck was to reach objects far away, it does not resolve the variability in apparent flexibility in those necks  while at the same time it supports finding that some terrestrial vertebrates tend to hold their necks in an upwards inclination , though not as high as  posits.
The value of biomechanical analysis over anecdotal is useful. I think the ecological aspects are interesting although problematic: Assuming a sauropod would not also walk 100m when food energy can be attained by lateral movement of the neck  (and not tested by [1,2]) during as little as 1/10th of that distance by increasing the lateral envelope of reach reduces the cost of movement in the body, placing it in the neck. By this standard, however, energy expenditure in moving the neck is low ( posit that as low an inclination as 30 degrees will result in virtually negligible expenditure of energy), so that movement laterally (not calculated) would have been low.
In conclusion, I find it unreasonable to assume that sauropods restricted their necks to a single plane of movement to feed; it is more reasonable to assume that if the neck was capable of moving in multiple planes to feed, and that either of these could be reasonable. Moreover, it is likely that the energy expenditure of moving the neck laterally during feeding while maintaining a mostly horizontal posture would cost less energy than raising the neck. The study does show that the neck was viable in a vertical extension of a feeding envelope, and this is always good.
Sauropods certainly traveled, however, and this would have required a great output of energy. The argument must then fall to whether sauropods maintained an inclined cervical position regardless of body movement, argued as positive in  and in news articles supporting . Sauropod neck posture while feeding could have even exceeded the median estimate for [1,2], while at the same time, a lower, safer posture could have been taken. And this is all without calculating the food available and amount required to produce the energy to perform these tasks. It seems far more efficient to use the least expensive method of movement and reach to attain food, and if food is evenly distributed as the paper argued to posit availability, then it should be laterally available as well, and this may require less energy than raising the head.
So the study purports what is possible, although it may be extrapolated to the what is likely with less (much less) data supporting it.
Update: I’ve completed a more thorough review of the topics in here, which can be found through this link, including a discussion of the various papers referred to below.
 Christian, A. 2010. Some sauropods raised their necks — evidence for high browsing in Euhelopus zdanskyi. Biology Letters (published online, June 2, 2010), doi: 10.1098/rsbl.2010.0359.
 Christian, A. & Dzemski, G. 2007. Reconstruction of the cervical skeleton posture of Brachiosaurus brancai Janensch, 1914 by an analysis of the intervertebral stress along the neck and a comparison with the results of different approaches. Fossil Record 10:37–48.
 Stevens, K. A. & Parrish, M. J. 2005. Digital reconstructions of sauropod dinosaurs and implications for feeding. pg. 178–200 in Wilson & Curry-Rogers (eds.) The Sauropods: Evolution and Paleobiology. (University of California Press, Berkeley.)
 Taylor, M. P., Wedel, M. J. & Naish, D. 2009. Head and neck posture in sauropod dinosaurs inferred from extant animals. Acta Palaeontologica Polonica 54(2):213–220.