The work is the first stage of a new approach to managing the city’s street trees following mediated talks between the council, Amey and STAG members.
The council says that out of more than 300 trees originally earmarked for replacement, it has already decided to "retain indefinitely" almost 90, and says "many more" could also be retained based on the on-street assessments.
The inspections are being carried out by tree and highways specialists using specialist equipment with STAG members in attendance, while local residents are being kept informed. The final decision to replace a tree will remain with the council.
Amey's Streets Ahead account director Darren Butt said: "Additional funding being provided by Amey will allow us to use new and existing engineering treatments in a much more flexible way, monitor trees closely and re-apply treatments where possible.
"As a result, we should be able to retain trees for an indefinite period as long as the highway remains at a good standard."
The council's cabinet member for environment and street scene Councillor Lewis Dagnall said: "The inspections are the first step in what we hope to be a promising year for the city’s street trees, where we will see a large proportion of trees, including the Vernon Oak and the majority of memorial trees, retained.
"We will also start work on a new street tree strategy in the first half of this year. We’re optimistic that by adopting a more collaborative approach, we will achieve a way forward which is beneficial for the entire city."
STAG representative Paul Selby said: "We welcome this new collaborative approach, which we believe will increase the number of trees that can be indefinitely retained, at the same time as increasing our understanding of the reasons why Amey and Sheffield City council say some trees cannot be retained.
"We encourage residents to come out and see the inspections taking place, if they are able to, to maximise the transparency of the work being done."