Residents and business owners are furious about the festering debris -including used sanitary towels, rotten food and burst bin bags - scattered around the back court of the Grantley Street surgery in Shawlands.
Shops and flats in Coustonholm Road, which share the communal garden area, are also affected by the mess and owners say it has been ongoing for years.
Rats and mice are attracted by the waste, with some finding their way into the nearby retail units.
David Anderson, manager of Vezza Barber in Coustonholm Road, installed traps in his shop after he spotted the vermin.
He said: "I don't know why the council hasn't cleared this. I've contacted them three times already.
"It's not so much the fly tipping, that doesn't attract vermin, but the rotting food does and it's not very nice."
Several shop owners have contacted Glasgow City Council about the mess but the situation has never been fully resolved.
A member of staff from the doctor's surgery said the stench is terrible and that it has contacted environmental health several times.
The junk is also posing a fire risk. A piece of wood in the courtyard blocks the entrance at Reilly's florist and would prevent staff from escaping a blaze.
Shop owner Marian Kinloch said environ-mental health officers came to visit the site nearly two months ago but it has made no difference.
Marian, who has been running her shop in Coustonholm Road for nine years, said: "We can't get out the back if something happens because of what has been left outside. The barber next door had a rat about a fortnight ago, and I've phoned them twice since then.
"Why do people want to live like this? I'm not paying someone to collect someone else's rubbish - it's from these flats."
Rob Fletcher, 31, who lives near the open ground where fly-tipping is rife said the Shawlands residents are fed up with the problem.
He said: "When the weather is hot, like now, the place stinks. It's unsightly and a serious hygiene issue.
"It's particularly bad that it's so close to the doctor's surgery. You want to think of a GP practice being clean, not clean at the front but littered with rubbish like a slum at the back."
A spokesman for Glasgow City Council said: "Bulk refuse is consistently being left in the court yard without anyone requesting the bulk uplift service.
"Letters have previously been sent out advising occupiers of the correct procedures for disposal of waste and advising enforcement action can be taken if people continue to dump bulk refuse in the back court.
"Environmental health today visited 218 Kilmarnock Road, 1 Grantley Street, 3 Grantley Street, 5 Grantley Street and 7 Grantley Street. They checked the back courts and bin areas and found no obvious signs of rodents."