South Africa's top tourist city Cape Town struggled on Monday to cope with flooding that affected thousands of people, cut off roads and forced shantytown residents to bale out water with buckets.

Relief officials said some 38,000 people have been affected since heavy rain began lashing the city a week ago, with damage estimated to run into millions of rand (dollars).

City disaster management spokesman Johan Minnie said it was the highest number of people hit by flooding in five years.

"We are stretched, especially in terms of supplying disaster relief. We are at capacity at the moment," Minnie said.

The rain has stopped but forecasters expect it to resume mid-week.

Many residents of tin shacks on the edge of Cape Town, home of South Africa's parliament, refused to move to emergency shelters, fearing their meagre possessions would be lost, he said.

Officials provided 25,000 meals to flood victims on Sunday.

Minnie said clean up would concentrate on clearing debris from storm water drains which have blocked roads.