Over Easter weekend four covers were stolen from St Albans Close, Wednesfield, leaving the drains "dangerously exposed".
Wednesfield North Councillor Phil Bateman reported the thefts to Wolverhampton Council's emergency team and Wednesfield Police.
He said: "These drain covers are being stolen at a rate of knots right across the city.
"Through this year and last, we have reported drain covers being stolen in Peach Road, St Albans Close (twice) and Eccleston Road."
Residents reported the thefts on Saturday.
Councillor Bateman added: "There were thieves about stealing drain covers in St Albans Close. Some members of the public contacted the city council and I understand four such covers were taken this time, leaving dangerously open the drains.
"The good news is when I contacted the emergency team this morning, they informed me that they had been out and made the drains safe."
Councillor Bateman wants local police officers to check scrap yards for drain covers to help apprehend the thieves.
Wednesfield Police team said: "We do pay regular visits to our local scrap dealers, and so do other neighbourhood teams in Wolverhampton, whereby we review their books.
"This is something the team will be made aware of and will keep this in mind when checking the books. Please if readers know who are behind these thefts, can you report the matter to the police."
Wednesfield resident Pat McAuliffe is furious with the thieves.
She said: "It’s disgusting that people take the drain covers where elderly and disabled people live. They could have a serious accident. Shame on them."
Alexandra Jones added: "Not the first in recent weeks in St Albans Close either, we noticed on the way to school a couple of weeks ago - it's so dangerous leaving them exposed.
"Scrapyards should refuse to take them. No market, no money!"