Ritchies-InterCity regional manager Malcolm Budd said the bus operator was fielding "hundreds of calls" from residents wanting to leave Christchurch.
The largest private bus company in Australia had transferred its South Island operations from Christchurch to Dunedin, with extra staff rostered on.
"They [the tourists and residents] want to get out ... either north to Picton, or south to Timaru, Oamaru, Dunedin or Invercargill."
The company was putting on more coaches to meet demand, with three full coachloads arriving in Dunedin daily, and more coaches added as they became available.
Air New Zealand chief executive Rob Fyfe yesterday said an extra 19 aircraft had been re-directed to Christchurch routes to cope with the demand.
The extra flights amounted to an additional 2500 passenger seats and brought the total number for Christchurch services up to 10,000 seats, he said.
"It's been a real challenge for us.
"We have shipped in 24 staff from other ports around the country to help deal with the overload."
All available seats on outbound flights from Christchurch International Airport were being snapped up and it was predicted to take another four days until flight capacity levels returned to normal, Mr Fyfe said.
Flights to Dunedin, Queenstown and Invercargill were in demand.
"We literally can't put any more capacity on.
"We are struggling to keep up with the flow of passengers," he said.
Mr Fyfe flew into Christchurch on Tuesday night on a flight chartered to bring back 40 Christchurch-based staff members, who had been on training courses in Auckland.
The concern for Air New Zealand's 1900 Christchurch-based employees was a primary consideration for the airline company, he said.
"We're still to establish if 30 of our staff are OK. It has been very tough for everyone ...
"Our employees have their own issues at home, like everyone else with power down and concerns about their friends and family."
Emergency assistance booths have been set up at Christchurch airport's international terminal by the Australian, United States, and Netherlands consulates, and New Zealand's Ministry of Foreign Affairs and Trade, to help stranded travellers.
Many tourists were trying to get out of the city, and inbound tour companies were moving operations out of Christchurch to Queenstown, and including Dunedin in their South Island itineraries.
Dunedin Visitor Centre team leader Louise Van De Vlierd said most people arriving in the city were staying with friends and family, but others were beginning to "come through" wanting places to stay.
Hundreds of Dunedin residents had contacted the i-Site to offer accommodation, and there was also capacity available at city accommodation providers.
"We are ready," she said.
