CARLETONVILLE, South Africa — Some 3,000 gold miners were trapped a mile underground today when falling pipe damaged the elevator, but the company began rescuing workers through a smaller shaft and estimated it would take 10 hours to get them all out.

There were no injuries and there was no immediate danger to any of the workers in Harmony Gold Mining Co.’s Elandsrand Mine, company and union officials said.

A health and safety chairman for the National Mineworkers Union, Peter Bailey, said the first 74 men reached the surface shortly after 1 a.m. Thursday. “They are all doing well,” he said.

The miners were trapped at a level slightly more than a mile underground when a column of water pipes fell down an elevator shaft causing extensive damage to the steel framework and electrical cables. Miners had to be evacuated with a smaller cage in another shaft.

One of the first miners rescued, Sethiri Thibile, clutched a cold beef sandwich and a bottle of water he was given when he reached the surface.

“I was hungry, though we were all hungry,” Mr. Thibile, 32, an engineering assistant who had been underground since 5 a.m., said. He said there was no food or water in the mine.

“Most of the people are scared and we also have some women miners there underground,” Mr. Thibile said.

After Mr. Thibile’s group rescued, Harmony’s acting chief executive Graham Briggs said that another 75 would be evacuated shortly, and after that they would be brought to the surface at intervals of every 25 to 30 minutes.

“It’s going to take some time because we are doing it carefully,” he said, adding the rescue could take 10 hours. “Nobody is injured, nobody is hurt, nothing like that at all.”

A regional chairman for the union, Deon Boqwana, said there was ventilation for the miners waiting below ground and officials were in contact with the men by a telephone line in the mine.

“They are still in good condition but are angry, hungry, frustrated and want to get out of there,” Mr. Boqwana said.

He said the miners were a little over a mile below the surface in a mine that at some points is about a 1½ miles deep. The mine is outside Carletonville, a town near Johannesburg.

Mr. Boqwana said the smaller cage being used to bring miners out can hold about 75 miners at a time. He said it normally takes three minutes to reach the surface but would be slower because rescuers were being careful. He said the evacuation would take about 10 hours.

Mr. Bailey, the union health chairman, said the miners were “very afraid,” hungry and thirsty after being underground for hours.

“Some of these mineworkers started duty on Tuesday evening. It is now Wednesday night and they are still underground,” he said.

A spokesman for the union, Lesiba Seshoka, said charged that the mine was not properly maintained.

“Our guys there tell us that they have raised concerns about the whole issue of maintenance of shafts with the mine (managers) but they have not been attended to,” he said.

Briggs rejected union criticism about safety conditions, and said the shaft was in very good condition with a lot of new infrastructure.

Last year, 199 mineworkers died in accidents, mostly rock falls, the government Mine Health and Safety Council reported in September.