Thomas said she has huge concerns for her son's safety.
"He is not himself. He is not acting or thinking properly and hasn't been right for some months," she said.
"I feel hopeless. I hope the police can find him and bring my boy home."
She implored the public to be on the look out for any signs of her son or his vehicle.
Finn Yeats is described as being approximately 180cm tall and around 85kg. He has very short red hair, blue eyes and is unshaven.
He is driving a silver 2006 Subaru Legacy with the registration JDR615, that has damage to the front left hand bumper.
"I just hope that if someone sees someone that they think might be him, can they go and talk to him and see who it is and if they are ok.
"Tell him to come home. Tell him he is loved and we want him back. Don't drive past and think 'oh, that might have been that kid' and not do anything."
Thomas said Yeats' car had been sighted at a toll road near Papamoa on Tuesday, but he has no known connections in the area.
"We have absolutely no idea where to start looking. Tuesday is a long time ago now, he could be absolutely anywhere," she said.
Police confirmed they received a missing person's report on Tuesday evening.
If you see Finn Yeats or his car, or have any other information, please call police on 111.
