Graber was born in 1940, and raised in South Shields, Tyne and Wear. She began her career as a teacher in Birmingham after earning a National Diploma in Fine Art from the Sunderland Art College (now part of the University of Sunderland) in 1959.
After twenty years of teaching, Graber first began to make animated films in 1970, initially using the medium to teach her students another form of art, following on from painting, clay modelling, woodwork and metalwork.
Between 1975 and 1980, Graber created a selection of animated shorts which were shown worldwide. One animation, Mondrian, about the Dutch painter Piet Mondrian was screened at the Tate Gallery, Mondrian’s own house in the Netherlands, the Open University and British Broadcasting Corporation’s children’s television series Blue Peter.
By 1975, Graber was working for Filmfair, and created the animation for Paddington Bear and Mr and Mrs Brown for the television series Paddington. She also animated the 1983 BBC series Just So Stories, adapted from a collection of children’s stories of the same name, written by Rudyard Kipling.
In 1980, newly divorced, Sheila left her role as head of Creative Studies at a large comprehensive school to begin teaching animation classes in Tunisia and Caracas, and pursue a career as a full-time professional artist and animator.
Many of Graber’s films are held in the archive of the Institute of Amateur Cinematographers film and video institute, including a number she made as the introduction for events and conferences hosted by that organisation.
In 2001, Sheila took a position at the University of Teesside, as the Animator in Residence. Commenting on her appointment, she said, “I’m hoping to work … on making a film and explore the potential of computer animation.” After creating over 60 shorts and three series for World TV, she teamed up with fellow director Jen Miller in 1996 to form the company Graber Miller. In 2004 she moved to the Republic of Ireland to open a studio to provide guidance and inspiration to a new generation of animators, before taking up a position at the University of Sunderland later that same year. Speaking of her role as Senior Research and Teaching Fellow in Animation, Graber said, “it’s great to work with older students. It’s a real two-way process and I hope I inspire them as much as they inspire me.” As of 2008, Graber continues to work at the university.