They were seen carrying off shoes, steering wheels, carpets, beauty cream and even motorbikes from beaches at Branscombe, Devon, apparently ignoring warnings that some of the containers may contain hazardous chemicals.
Goods worth thousands of pounds were washed up after the stricken MSC Napoli was deliberately beached about a mile offshore.
Police warned that those who take away goods and fail to report they have done so are committing a criminal offence.
They closed Branscombe to all visitor traffic, as well as roads leading to the beach, in an attempt to stem the flood of curious beachcombers.
Mark Clark, of the Maritime and Coastguard Agency (MCA), said up to 40 containers have come ashore.
He said: “We are concerned about the mass hysteria being shown by people ripping everything they can out of containers.
“You do not know what is in the containers, we just want people to understand some of the risks they are running.”
One local woman salvaged carpets for the home she is decorating.
Preparations to pump up to 3,500 tonnes of fuel oil from the ship will resume today after engineers were delayed by technical difficulties.
The treacle-like oil on board the 62,000-tonne Napoli will have to be heated before it can be run down lines into waiting vessels.
The operation to remove the oil is the first step in securing the ship which lies on a sand bar off Sidmouth.
Fears remain over the environmental impact of the containers and up to 200 tonnes of oil from the vessel’s engine room on the world heritage coastline.
Once the oil is removed, two cranes will be brought in on barges to remove some 2,400 containers that remain aboard the Napoli.