Australians have emailed MPs with dozens of requests for free portraits of the Queen, after the little-known entitlement was publicised this week.

Under official rules, citizens may ask for "nationhood" material - things such as Australian flags, anthem recordings, and portraits of the head of state.

One MP, Tim Watts, said most requests for images of the Queen were due to a case of "excellent trolling".

It followed a Vice story that had drawn wide attention to the entitlement.

"I can say before the story was published, I had received zero requests for portraits of Her Majesty Queen Elizabeth," Mr Watts told the ABC.

"The last 24 hours, I would say [I have received] about four dozen. I think 99% were tongue firmly in cheek."

Other lawmakers also noted the influx of requests, with some making light of it.

Under the "Nationhood Material" entitlements, Australians can also ask for a portrait of the Duke of Edinburgh.

Some people on social media complained that frivolous requests were "taking up valuable time and money".

Mr Watts said it was more common to supply constituents with flags, including the Aboriginal and Torres Strait Islander ensigns.

"Usually people request flags when they're representing Australia overseas for sport or school or community groups," he said.

Australia is a parliamentary constitutional monarchy with the Queen as its head of state. She is represented in Canberra by an appointed governor-general.

The nation voted against becoming a republic in a 1999 referendum, but some politicians say the debate should be revisited.