Digging a trench around the site is the only way to prevent hungry animals from eating rubbish at the site that measures 800 square metres, a Wildlife Ministry spokesperson told the DPA news agency.
A post-mortem examination has yet to confirm the cause of the recent death of two elephants.
More than 20 elephants have died in a similar manner during the past eight years.
The two elephants who died recently made headlines in the country after images of the animals among the rubbish went viral.
A video of wildlife officials pulling plastic from the rectum of one of the animals was also widely shared.
Wildlife activists have called for greater efforts to protect elephants as about five die annually under similar circumstances.
There are more than 50 rubbish dumps throughout the island country.
However, many more elephants die in Sri Lanka after being injured by explosive devices, electrocuted by electric fences or shot, with most of the deaths due to farmers.
Habitat loss is also harming the animals and elephants are destroying more and more fields and houses.
Some are also killed by poachers who want their tusks.
According to official figures, a total of 369 elephants died of unnatural causes last year.
There are about 6000 elephants in Sri Lanka, according to the last census 10 years ago.
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