At least five home-made snares have been spotted in a field owned by Peterborough City Council near Fletton Cemetery in the last two weeks.
RSPCA chiefs believe they have been set to catch rabbits and foxes, but the area also includes football pitches used by city youths.
Police have warned youngsters to take care to avoid being caught in the copper wire traps.
A spokesman for Cambridgeshire Police said: “There is a real danger that a small child could wander into them and sustain a nasty injury.
“We ask parents to make sure children are aware of the danger these snares present and to make sure they are careful when playing in the area.
“Animal snares are illegal unless they are used on private land as part of a pest control regime.
“There is no reason for these traps to have been placed in this area.
“It is a wholly irresponsible thing to do. We would appeal to anyone with any information about these traps to contact police.”
Three snares have been removed by the RSPCA this week after they were found in and around the edge of the cemetery.
Another was found by a man whose daughter was walking her Staffordshire bull terrier in the area.
The man, who asked not to be named, spotted and removed a trap from the area on Monday afternoon.
When he and his daughter, Melanie Young, from Eye Road, showed The ET where the snare was found, another was spotted by our photographer David Lowndes.
Mrs Young (39) said: “They are made of welding wire and copper that could easily cut into the skin.
“It would catch your hand or foot, so children should be very careful when they are playing nearby.”
Mrs Young added that she and her father have both seen evidence that people are living rough in the area.
She added: “In the last few weeks we have seen people there who look like they are living in the bushes.
“There are also empty vodka bottles scattered around which there didn’t used to be. Now there are these snares being put around.
“We are thinking of going somewhere else for dog walks because it does not feel safe.”
The RSPCA has teamed up with the council and police to investigate who is setting the traps.
RSPCA inspector Justin Stubbs said: “Traditionally, people snare rabbits to protect crops or to catch them for meat. In that area there are no crops so they seem to be trapping them for their meat.
“We do not know who has been putting the snares down.
“There is a concern that where the snares have been set they could end up catching non target species such as cats or even small dogs. We often get reports of cats, dogs, badgers and even deer caught in them.
“Our research shows that only a third of the animals caught in snares were actually the species intended to be caught – we would like to see snares banned.
Both the RSPCA and the police have increased checks in the area to catch the people setting the traps.
Anybody with any information should call the RSPCA on 0300 1234 999 or the police on 0345 456 4564.