The man and woman are believed to have been from Crewkerne and Taunton in Somerset. One of the victims has been named locally as Rosemary Snell.
The car was only found after Avon and Somerset Police raised the alarm, prompting Dorset Police to search the area around Beaminster Tunnel. Avon and Somerset Constabulary used telephone and bank card data to track the couple to the local area.
Emergency service crews were then sent to search the tunnel and discovered a car buried under mud.
The roof of the car had been crushed by several hundred tonnes of earth and it has now been taken away from the scene. Police have already found one body in the car and say they are expecting to find another upon further investigation.
Rosemary Snell, who was in her 60s, was found in the car. She was well known in the village of Misterton, near Crewkerne in Somerset.
Ms Snell, who played an active role in the local branch of the Women's Institute, was reported missing, along with an unnamed man.
"I think everyone knew her in the village," a villager said.
"She had a magnificent spirit and was most enjoyable company socially. Everyone will be terribly shocked by this."
Assistant Chief Constable James Vaughan from Dorset Police explained why it had taken so long to find the car in the collapsed tunnel:
Assistant Chief Constable James Vaughan said that Dorset Fire and Rescue, county engineers and Dorset Police, working together, brought in heavy machinery yesterday evening and began to excavate some of the mud at the front of the tunnel.
Assistant Chief Constable James Vaughan went on to say nobody suspected that people had been trapped in the tunnel and that "it wasn't obvious in any way, shape or form that a vehicle was there...it's an unsafe structure and needs to be properly looked at by engineers."