Dr Elder's areas of research expertise are in 20th- 21st century Australian cultural identity, especially relations between Indigenous and non-Indigenous peoples in Australia. In particular she has intensively explored some of the ways in which non-Indigenous peoples think about belonging and has analysed both the pleasure and anxiety that inform narratives of national belonging. Specific projects have focused on assimilation in popular fiction; whiteness and government immigration and Indigenous policy in the 1950s and 1960s. This work has drawn on and contributed to the development of Critical Whiteness Studies and Settler Colonial Studies in Australia.
One current research project focuses on race, identity and the Australian historical television mini series (1970-2005). Dr Elder is exploring representations of belonging that are produced through television dramas about colonial history. Other areas of research include (post)reconciliation, nationalism and sexuality, and women and non-professional work in the 1950s-1960s.