Graeme Beveridge won his first cap for Scotland when he replaced Andy Nicol during the second Test of the 2000 summer tour to New Zealand. Before the tour Beveridge played in the non-cap match against the Barbarians, having been chosen for the senior Scotland squad for the first time for the match against France in March 2000.
He went on to win his second cap as a substitute against the USA in the first autumn Test that same year.
Graeme was in Scotland's under-19 team at the 1995 FIRA Junior World Cup in Bucharest and is also a former under-19 and under-21 international captain. He was in Scotland's squad for the 1996 Students’ World Cup in South Africa, and the following year, as an emergency replacement, he joined Scotland's touring squad in southern Africa in time to play in the final-match win over Eastern Province.
A leg injury kept him out of Glasgow Caledonians' early matches in 1998-99, but he recovered in time to make a try-scoring debut at A international level in the runaway win over Italy at Netherdale in March 1999.
Graeme also played as a replacement in the A international against France the following month, while in 2000 he added to his A appearances against Italy, Ireland, Wales and England.