Essex Police, the Helicopter Medical Emergency Service (HEMS) and the East of England Ambulance Service's Hazardous Area Response Team (HART) also attended the incident, which happened at about 18:35 GMT.
Fire service watch manager Glenn Jackson said crews had to help the third man into the tumble dryer before being able to remove the door and release all three.
"We used a range of equipment to free the casualty's ankles and allow him to crawl into the tumble dryer," he said.
"The HEMS team gave him pain relief and we then managed to move the door, again using a range of equipment, so the men could crawl out."
Mr Jackson said crews "worked really hard in arduous conditions".
"It was a difficult site to access and we had to carry a lot of heavy equipment a large distance from the appliances to the tumble dryer and then use our expertise to free the men safely."