The move is part of the biennial Rock On Scottish geology festival, which aims to raise awareness of Scotland's impressive geological heritage. The next festival will be held in a year's time. The competition is a way of acknowledging the Scottish stone used in the new building in Edinburgh.
It is open to pupils aged under 18. Using a maximum of 25 words, they must write something about Scotland's landscape in prose or any poetical form, including haiku or ode.
Winners in both English and Gaelic language will be selected, although only the overall winner's name and entry will be carved in stone, in both languages, outside the landmark building.
The organisers are hoping for a number of Gaelic entries, not least because Gaelic-speaking areas have so many fascinating geological sites.
The flagstone to be engraved with the winning text, which will be unveiled in late January, was formed from thin layers of silt, built up at the bottom of a lake that once stretched from Caithness to Orkney and Shetland around 380 million years ago.
This was one of many ancient landscapes and environments that have occurred during Scotland's eventful 3,000 million-year journey across the planet, the story of which is written in Scotland's rocks.
Sarah Roe, of Scottish Natural Heritage, hopes the competition will ignite an interest among teachers and pupils in what is often regarded as a dry subject.
"We've found that by making geology fun and emphasising the exciting aspects of the subject, we can really get kids interested," she says.
"Children are fascinated to discover the different ways landscapes have been formed here and that there were once volcanoes, tropical seas, deserts and rainforests, each leaving a legacy of rocks from which Scotland's landscape is fashioned.
"Arthur's Seat, in Edinburgh, is a unique example of a volcanic landform and is a great landmark to show children."
She says geology can be exciting to children if you can engage them and explain how landscapes that were billions of years in the making have affected the people living there. Scotland's underlying mineral wealth, including oil, coal and iron, has helped to make it wealthy and industrialised.
In addition to organising the festival in partnership with the National Museums of Scotland and the National Geological Survey, Scottish Natural Heritage has funded a series of geological trails in the Cairngorms. In particular, Knockan Crag, near Ullapool, which has an interpretation centre describing the area's rock formations, is increasingly used as part of school field trips.