Police have launched extensive LandSAR searches for Beattie, focusing on areas including the Ashley River and Hillcrest Rd in Fernside.
Senior Sergeant Paul Reeves, who is in charge of the missing person's investigation, said the search was being conducted in close proximity to the family's address and teams were searching the riverbed as well as outbuildings on nearby properties.
On Wednesday Reeves said there was a possibility that Beattie had left the area but searches would remain in Fernside unless new information came to light.
Beattie has long blonde hair, and is believed to be wearing orange and black Nike shoes.
Police are continuing to appeal for sightings of Beattie. Anyone who may have seen he is urged to contact police immediately.