Elaine A. Moore studied chemistry as an undergraduate at Oxford University, England, and then stayed on to complete a DPhil in theoretical chemistry with Peter Atkins. After a two-year postdoctoral position at the University of Southampton, England, she joined the Open University, UK (OU), in 1975, becoming a lecturer in chemistry in 1977, senior lecturer in 1998 and reader in 2004. She retired in 2017 and currently has an honorary position at the Open University.

She has produced OU teaching texts in chemistry for courses at levels 1, 2 and 3 and written texts in astronomy at level 2 and physics at level 3. She is a co-author of Metals and Life and of Concepts in Transition Metal Chemistry, which were part of a level 3 Open University course in inorganic chemistry, and were co-published with the Royal Society of Chemistry. She was team leader for the production and presentation of an Open University level 2 chemistry module delivered entirely online. She is a Fellow of the Royal Society of Chemistry and a Senior Fellow of the Higher Education Academy. She was a co-chair for the successful departmental submission of an Athena Swan bronze award.

Her research interests are in theoretical chemistry applied mainly to solid-state systems, and she is the author or co-author of more than 50 papers in refereed scientific journals. A long-standing collaboration in this area led to her being invited to help run a series of postgraduate workshops on computational Materials Science hosted by the University of Khartoum, Sudan.