WARNING: Some readers may find an image attached in this article distressing.
The rabbits were discovered by Burdiehouse Burn near Gilmerton Dykes Crescent, Edinburgh by a member of the public on Monday.
The animal welfare charity is now appealing for information from the public as it releases distressing images of the animals.
Anyone who knows the identity of the owner or the rabbits themselves are being asked to get in contact with the SSPCA.
John Toule, Scottish SPCA senior inspector, said: “One rabbit was tan and the other was white with small black markings.
“Their bodies had been left on blankets and attempts had been made to cover the rabbits’ bodies with a cardboard box.
“The rabbits were not microchipped.
“If anyone has any information on the owner of these rabbits, or the rabbits themselves they can contact our confidential animal helpline on 03000 999 999.”