Mr Anderson, 25, was last seen getting petrol at the BP service station on George Street at 11.30am on Thursday.
The alarm was raised after Mr Anderson failed to answer calls and texts to his mobile, which friend and family spokesman Paul O'Sullivan said was "extremely unusual for a guy who is on his phone 24/7."
"He's really quite social and always responds really quickly."
Mr O'Sullivan said Mr Anderson's "distressed" mother had travelled from Oamaru as well as extended family from various parts of the country to help with the search.
"Brad's mother, family and friend's are all devastated by his disappearance and we need to find him and bring him home.
"We need help from the public to find out where Brad drove to after he left the service station...in our best case scenario, we're all hoping Brad's out there and will call us when he hears this message."
Mr O'Sullivan said Mr Anderson, an IT-consultant at Otago University, was not the type of person to go away without notice.
"It's very out of character to head off and not contact anybody. He is always in contact with people. There is always texting happening and he hasn't made any kind of contact like that at all."
Friends and family have posted messages on Facebook asking for help to find Mr Anderson, and the family has also tried to find him by tracking his cellphone signal which is still transmitting from within 30km radius of Dunedin's Mt Cargill.
The family yesterday also had a helicopter conducting an aerial search and people combing the city.
Mr O'Sullivan said Mr Anderson had not touched his bank account since he got petrol on Thursday, and the last image of him was from the station's security camera.
Police believe Mr Anderson is in the greater Dunedin area, travelling in a silver 2000 Nissan Wingroad stationwagon, registered number EJK998, with "IT Otago" signs on its sides.
They have no leads yet, but are working on narrowing the search area.
Mr Anderson is described as 186cm tall, of thin build with blue eyes and short black spikey hair.
He was last seen wearing blue/grey coloured jeans, a light blue "V" neck t-shirt, and a navy-blue coloured hooded sweatshirt with a red print.
Anyone with information is asked to contact police.
