[1] Burlinson's first public appearance as an actor was as Colonel Pickering in Mosman Primary School's production of My Fair Lady.

By the beginning of 1979, he began playing Mickey Pratt in the teen-oriented Australian soap opera The Restless Years, a role which lasted 16 months.

In 1978, he appeared as Charlie in the Old Tote Theatre Company production of Da and as Jud Templeton in the play Tribute in 1979.

[citation needed] In 1981, Burlinson had his career break when he was given the main role in the biggest Australian film production ever, which was to be shot the next year, The Man from Snowy River, as the title character, Jim Craig.

In his next film, Burlinson portrayed horse trainer Tommy Woodcock in Phar Lap: Heart of a Nation.

From then onwards, Burlinson focused on historical productions, including the highly acclaimed 1988 LWT mini-series Piece of Cake, set in England in 1939 and based on the 1983 novel of the same name by Derek Robinson and the Canadian Western drama film The Legend of Kootenai Brown retitled Showdown at Williams Creek in the United States, set in pioneer North America.

He appeared on TV in 1990 on Ray Martin's Midday Show to nervously debut his singing voice to the Australian public with the song he had written, "The Man in the Hat".

In 1996 he had stage roles with the Sydney Theatre Company, starring as Franklin in Merrily We Roll Along and as Ricky in Miracle City.

In 1998, Burlinson created Frank – The Sinatra Story in Song which opened at the Seymour Centre in Sydney before going to other major cities.

[4] Burlinson returned to the world of theatre in April 2004 in the lead role of Leo Bloom in Mel Brooks' musical The Producers.