The sad scene was discovered by contractors of Arun District Council in Littlehampton Cemetery in Horsham Road, Littlehampton, today (May 27).
Two black bags filled with the bodies of the four reptiles had been stuffed into a bin.
According to the council, it is believed the snakes may have been frozen to death.
A spokesman said: "We are shocked by this horrendous act. If you have any information that would help investigations email [email protected]"
According to a tweet by the council, they were boa constrictors - two albino, one black and one reddish-coloured - each between 1.5m and 2m long, weighing approximately five to six kilograms.
Boa constrictors are non-venemous snakes that can be found in Central and South America and are often kept as pets in the UK.
According to National Geographic, in the wild the species can grow up to 4m long and weigh up to 45 kilograms.
The reptile is known for its method of killing and eating its prey: wrapping its muscular body around the victim until it suffocates, and unhingeing its jaw to swallow it whole.
In the wild, this will include birds, monkeys, and wild pigs.
It is understood the incident is being reported to the RSPCA and Sussex Police.
A spokesperson for the RSPCA “It is really sad to hear what has happened to these poor snakes and we would urge anyone with information to contact us or the police with information.
"Sadly, we are often called to rescue reptiles. Unfortunately, many people are unaware of how much of a commitment reptiles are when they take them on.
“Many people do not realise what they are taking on when they buy these pets so we are urging prospective buyers to do their research before getting one. Potential owners of reptiles must thoroughly research the needs of the particular species and what is required in the care of the animal, using expert sources, and only consider keeping one if they can ensure they are fully able to provide for these needs.
“We have produced care sheets for a number of exotic pet species, they can be found on our website.”
Anyone with information about what may have happened can call the police on 101 or report it online.