Elizabeth Timar, 18, was last seen near Blackpool Sands at 19:45 BST on Monday.
Romanian Ms Timar, from Exeter, had been "at the beach for the afternoon with a male", said Devon and Cornwall Police.
The force has carried out a major air and sea search with help from RNLI coastguards and Dartmoor Search and Rescue Group.
Ms Timar was last seen wearing a black coat with a red top underneath, blue jeans, and carrying a handbag.
A force spokesman said: "If anybody was in the area on Monday and saw a young female acting strangely then please get in touch."
Concerns are growing for a teenager who was last seen at a beach in South Devon six days ago.