The model of a baby T-Rex in an egg is part of the Exmouth Dino Trail in Devon and parents have reacted with horror to the image which was posted on social media.
One parent said: “I worry as children play with these dinosaurs, I was disgusted.
“I feel sick to think that children are anywhere near that.”
The model had already been damaged by vandals this month.
Organiser of the Exmouth Dino Trail, John Thorogood, said: “I saw the image on social media and was completely disgusted by it.
“It was clearly a deliberately posed photograph of a very immature adult engaged in a sex act.”
Mr Thorogood added: “Whilst we have had some deliberate damage to the dinosaurs in past weeks, this episode brings things to an all time low as far as these important and very popular assets to our town are concerned.
“I hope the police are successful in tracing this woman and dealing robustly with it.”
Other incidents of mistreatment of the models includes a life-sized Stegosaurushaving its tail removed in August.
The fibreglass sculptures trail officially launched on Sunday, August 21, and is designed to highlight the resort’s connection with the Jurassic Coast, which stretches from Orcombe Point at the end of the seafront to Portland in Dorset.
According to The Sun, police have launched a probe to identify the woman pictured.