The university's executive board will vote today on proposals to either shut the department completely, reassign a limited number of postgraduate courses to other departments, or retain it in its current form.
A protest rally was held in support of the department's staff and students outside the Firth Court buildings on the campus today, and a Change.org petition has been signed by wellwishers from all over the globe.
Sheffield is considered to be one of the 50 best archaeology schools in the world and its staff are currently affiliated to a major excavation at Stonehenge alongside working on more local projects.
The department was founded in 1976 but its members believe the subject has suffered from a 'corporatisation' of higher education since tuition fee rises, which has driven students towards degrees with higher employability prospects such as business, law and finance.
As a result applications for undergraduate courses have fallen, despite academics being prepared to lower the A Level points tariff for entrants, although postgraduate programmes are still performing well and attracting international students.
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."