The unique lattice-style design has been created by RMJM Architects, an international firm responsible for the university’s Information Commons building next to University Square roundabout.
The building will be created on the site of the former Jessop Hospital and will spell the end of the Grade II-listed Edwardian wing of the old hospital, which is currently derelict.
The original, Victorian wing of the hospital remains and has been converted to house the university’s music department.
The university says it needs to demolish the Edwardian wing because the engineering building would otherwise not be big enough for requirements.
Keith Lilley, director of facilities and estate management at the university, said: “I think the new building will be stunning.
“It will provide a huge opportunity for the city to celebrate its heritage by creating the engineers of the future.
“It creates a really positive statement about Sheffield.”
The university is submitting a planning application for the new building to Sheffield Council this week.
Its management says demand for engineering places is continuing to grow from both UK and overseas students, despite an overall fall in applications nationally due to the rise in university tuition fees.
The university is currently spending £1 million on temporary buildings to provide extra capacity for the engineering faculty during the next five years.
Mr Lilley said: “The new building is vital for the future. It will provide capacity for up to 5,500 students at any one time and will house teaching space plus laboratories and study areas.
“Importantly, construction of the new building will also allow us to embark on a £56 million refurbishment of accommodation housing the existing engineering department, such as the Sir Frederick Mappin Building.
“We cannot refurbish those buildings at present because we would have nowhere to put the students while work is carried out.”
Describing the layout of the planned building, Mr Lilley said the lower ground floor would house seven lecture theatres with capacities of up to 400.
The ground floor would be used for teaching space, a cafe and ‘pilot plant room’ used for practical classes and which would be visible from the street to showcase the faculty’s work.
The upper four storeys would be used for workshops, study areas and computer rooms.
Mr Lilley said that suspended within a central glazed atrium between the main floors would be numerous ‘floating’ classrooms and study areas on the upper floors.
He said: “This will be the biggest-ever investment by the university in new buildings, with the previous largest investment being the refurbishment of the Arts Tower at a cost of £36 million.”
The university hopes its plans will be considered for approval at a Sheffield Council planning board meeting in December.
A contractor would then be chosen in the spring, with construction expected to take less than two-and-a-half years.