The animals were hit when their herd was crossing railway tracks in the Rambha forest area, a railway spokesman, RN Mohapatra, said.
The state’s wildlife department said its warning asking trains to slow down because elephants were moving in the area was ignored.
Nearly 300 elephants have been killed in Orissa in the past five years.
Most of the deaths have been blamed on accidental electrocutions, poaching, poisoning by farmers to prevent them from damaging crops and being run over by trains.
The state government recently set up a committee to monitor elephant deaths.
While elephants are worshipped by many in India, shrinking habitat has led to increased conflict with people and the deaths of many of the protected animals.
There are around 26,000 wild elephants in India, where it is a heritage animal.
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