The blocks in Gracemount - Gala, Soutra and Fala Courts - are due to be demolished on Sunday October 25th.
Three local schools - Gracemount, St Catherine's and Kaimes - are taking part in the competition which is based around 'safety'.
The schools are being given a presentation by staff from the Project Team and contractors Coleman & Company about safety issues around the site.
A judging panel will then choose the winning poster and the child will get the chance of a lifetime to push the demolition button.
Michelle Fraser, Project Manager for the City of Edinburgh Council, said: "The contractors will still be on site for several months after the multi storey blocks come down and it's extremely important the children fully understand the dangers of going near the demolished area.
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"It is also important that the children continue to be aware of the dangers associated with demolition and building sites through the period of site clearance and also the construction of the new homes next year.
"The project team thought it would be a great idea to combine the poster competition around the safety aspects and to give the winning child the chance to push the button."
James Howard, Strategic Development Manager from Coleman & Company, added: "It will be good to talk to the schools and getting the children interested in demolition and recycling, whilst at the same time making them aware of how they or their friends can get hurt if they see sites as a playground.
"We are really looking forward to seeing the entries for the art work competition and wouldn't it be great if a few of the children go home, after our assembly talks, saying they want to work in demolition when they grow up."
Councillor Paul Edie, City Housing Leader, commented: "The redevelopment of Gracemount will see the first new Council homes being built for a generation as we try to plug the gap of affordable homes in the city.
"We want good quality affordable housing in mixed developments throughout the city built to 21st century standards and Gracemount is the first huge step forward to achieve this vision."
(GK/BMcC)
