Drummoyne Public School posted the new rule in a newsletter on its website, saying such activities cannot be condoned during lunch and recess breaks.
The school said the State Schools Sports Unit had advised that "such activities are prohibited unless under the specialised supervision of a trained gymnastics teacher with the correct equipment mats".
But parents have described the rule as extreme, with parent Rebecca Chown collecting more than 250 signatures on a petition demanding the rule be overturned.
"It's ridiculous. What's the world coming to when kids can't do handstands and cartwheels at lunch time?" she told The Daily Telegraph.
The Education Department says school playground rules are set at school level to prevent injury but there is no departmental ban on play activities such as handstands, cartwheels and somersaults.
What do you think about Drummoyne Public School's decision to ban cartwheels and handstands?
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