The university's management will make a decision on the future of the department, which was founded in 1976 and is rated as among the top 50 in the world, next week and academics believe they favour a complete mothballing of archaeology degree courses and redundancy of staff.
Another option being considered is a partial closure with some programmes, mainly taught Masters courses, and a small number of staff being assigned to other departments.
Sheffield archaeologists have been involved in numerous excavations across Yorkshire, including the digs at the Sheffield Castle site in 2001 and 2017, and also run short courses for the general public. They work with organisations including the Peak District National Park and run community events.
A crisis in undergraduate recruitment on a national level has seen applications for first degrees in archaeology reduce in line with tuition fee rises, although department sources say this shortfall has been made up by an increasing number of postgraduate students from overseas.
Professor Umberto Albarella, who joined the department in 2004, said the threat came against the backdrop of the government incentivising subjects such as science and engineering at the expense of arts and humanities.
During his tenure, the number of permanent teaching staff has fallen from 29 to 11.
"There is disappointment and shock, and it's seen as hostility from the management. We didn't expect the decision so soon. Regardless of personal concerns about jobs and income, we feel very strongly that closure would not be in the best interests of the university.
"We feel as if politically, arts and humanities courses are being devalued. There have already been responses from all over the world and we warned the university that they had underestimated our value and the support for us.
"The department has made an immense contribution locally - we are hands-on and practical. Since tuition fee increases, there has been a recruitment crisis because archaeology is a subject that people choose because it is their passion, not for money - it will not make you rich. We had asked the university if we can reduce the A Level results tariff, which would enable more students to apply, but they refused.
"We do a lot of outreach work with schools and museums, and we've taken part in so many initiatives in the community. We've had so many messages from people who have done our short courses and are in shock at the news.
"As a department, we've been eroded and undermined and it's been a catastrophic failure of management over a number of years."
Professor Albarella's views are echoed by the Sheffield branch of the Universities and Colleges Union (UCU).
A spokesperson said: "We will strongly defend any cuts and the archaeology department has our full support. We have considerable concerns about jobs in arts and humanities departments. Across the universities sector, these departments are under real threat as the current government values STEM subjects.
"It's a marketisation of education that undervalues the skills and experiences to be gained from studying these subjects."
A petition set up to save the department can be viewed here.
A University of Sheffield spokesperson said: "The University of Sheffield has undertaken a review of its department of archaeology. Staff and student representatives participated in the review, and no decisions have been taken."