Employers fear they will not be able to find enough highly-skilled workers, says the business lobby group, the CBI.
It says demand for these types of workers will rise with the recovery, but half of employers think they will not be able to find the right people.
It surveyed almost 700 bosses across a range of companies, who together employ 2.4 million people.
They fear the right type of graduates will not be available to meet business demands.
But even getting people with the suitable A levels was a worry for a third of businesses.
The CBI predicted in its report 'Ready to Grow: business priorities for education and skills', that as demand for qualified people rose, those without skills would be less in demand.
And despite the recession, nearly half of employers said they were already having difficulty recruiting staff with skills in science, technology, engineering and maths, with manufacturers and science-related businesses finding it hardest to find staff.
The CBI's director general Richard Lambert urged the new government to take a lead.
He said: "In the future, people with qualifications in science and maths will be particularly sought after, and firms say it is already hard to find people with the right technical or engineering skills.
"The new government must make encouraging more young people to study science-related subjects a top priority."
Business leaders were asked for tips as to which subjects that would be most likely to lead to a job.
A total of 42% of bosses, who responded to the survey, said young job seekers should pick business studies, while 21% thought Maths was best for career prospects and 13% said English.
Psychology and Sociology were at the bottom of the list of requirements.
The survey shows employers remain committed to providing apprenticeships, despite the recent recession.
The highest provision is in construction (78%) and manufacturing (56%).