Out of 15 shops visited by underage customers in Stocksbridge, Walkley, Crookes and Upperthorpe, six illegally sold items to children.
The operation was organised after a rise in reports of anti-social behaviour and incidents involving fireworks.
PC Sarah Forsythe said: “The purpose of test purchase operations is to see whether businesses are selling items, such as alcohol, knives and, at this time of year, fireworks, to people they shouldn’t be.
“Out of a total of 15 premises, six failed, with rockets, beer and knives all being sold to underage volunteers.
“In one of the shops, a set of six knives were sold to one of our teenagers without any challenge at all.
“Another one refused to sell fireworks without ID, which is great, but just moments later our volunteer managed to buy alcohol from another till.
“One of the premises, a hardware store in Upperthorpe, is a repeat offender and is in the process of being referred to trading standards by our officers. There are, and should be, consequences if people are ignoring the law.”
Sheffield’s Chief Inspector for Neighbourhoods, Helen Lewis, said: “I want this to be a warning to businesses that we do take underage sales seriously, especially where potential weapons are involved.
“At this time of year, we know that fireworks are used to cause fear and distress to our communities, and this is one of the ways we are trying to prevent this from happening.”