Calls have been made for the SNP Government to relax restrictions on the number of home-grown students going to Scottish universities.
Scottish Labour want the cap reviewed after it emerged that Dundee and St Andrews universities accepted less than half of the applications made by Scots.
Iain Gray, the Labour MSP, said Scots are being “locked out” from studying in their own country because of restrictions imposed to minimise the strain on the public purse from free tuition.
He said: “Universities have increased places for students from the rest of the UK and outside the EU, but have not been allowed to do so for Scottish students.”
Just over a third (35%) of applications for undergraduate courses from Scottish students to St Andrews were successful in 2015, according to the figures from Audit Scotland.
At Dundee, the offer rate was 45%, while Abertay approved the highest proportion of Scottish applications in the country at 77%.
Across the country, 8,885 Scottish applicants, out of a total of 47,710, did not receive an offer at any home institution.
Audit Scotland said it has become more difficult for Scots to secure places, as applications outpace the offer rate.
A spokesman for St Andrews University said: “Restricted numbers have always been a consequence of the current Scottish system, but we are committed to work with the Scottish Government on a shared objective of ensuring that as many bright young Scots as possible are able to benefit from a university education.”
A Dundee University spokesman said more than 70 per cent of their undergraduate community have Scottish fee status.
“The fact we attract thousands of talented students from around the world is a sign of our continuing success, as is the demand from Scottish students for high-demand, capped places at the University of Dundee,” he added.
A Scottish Government spokeswoman said: “We remain firmly committed to ensuring that tuition is free for first time Scottish and EU domiciled undergraduate students.
“Over 120,000 students are supported in this way every year. This direct government investment helps ensure that average student loan debt in Scotland is the lowest in the UK.”