The report claims it is "not easy or automatic" for qualified engineers to find related employment in the UK.
Concerns over a lack of good quality science and engineering graduates have regularly been raised by employers in the UK.
But research from the Birmingham University challenges this point of view.
Their report titled Is there a shortage of scientists? analysed figures from 1986 to 2009 from the Higher Education Statistical Agency on the proportions of engineering students entering related jobs, other professions or work that did not require a degree in 2009.
It suggests that about 46% (less than half) of 2009 engineering graduates were in jobs directly related to their degree subject six months after leaving university.
20% were employed in roles that were not directly related to their degree and 24% were in "non-graduate" employment, for example working as waiters or in shops.
"Perhaps, because of recent initiatives, there seem to be too many people studying science for the labour market to cope with, or perhaps graduates are no longer of sufficient quality,” says the report.
"It is more likely, however, that all of these scientists are without relevant employment every year because the shortage thesis is wrong and there are no jobs waiting for all of them or because they are 'dropping out' having learnt that they do not enjoy their subject areas."
Report author Professor Emma Smith added: "It is astonishing, in the light of claims of science graduate shortages, that so few new graduates go into related employment.
"The figures suggest it is not easy or automatic for qualified engineers to get related employment in the UK, despite the purported shortages."
What can be done to ensure that young people can enter positions that they have trained to do?