Montrose Coastguard Team and both Arbroath lifeboats were scrambled in the early hours of Sunday morning.
The alarm was raised around 3.15am to reports of six people having been cut off by the tide at the cliffs at Auchmithie.
A spokesman for Arbroath RNLI said: “Once on scene the casualties were quickly located and the inshore lifeboat was able to transfer the six casualties to the all-weather lifeboat.
“Both both boats then returned to station and were made ready for service again.”
The UK Coastguard said the six people who were cut off were safe and well.