Dr Rebecca Shipley's research career started within the Oxford Centre for Industrial and Applied Mathematics, University of Oxford, where she received a First Class Honours Masters degree (Mathematics), before completing her DPhil (PhD) working on multiscale mathematical models of blood flow and drug delivery in vascularised tissues. During this time, she developed a passion for interdisciplinary research around the application of mathematical models in medicine. In 2008 she took up a Junior Research Fellowship at Christ Church College, University of Oxford, to develop mathematical models that describe biomechanical and biochemical stimulation of tissues. Dr Shipley also gained practical experimental experience through two concurrent Visiting Research Fellowships at the Centre for Regenerative Medicine, Bath, and Tissue Repair and Engineering Centre, UCL. Her research on integrating mathematical models with experimental data inform the design of bioreactors for tissue engineering led to the award of Young Researcher of the Year for the UK Tissue and Cell Engineering Society in July 2011. 

In May 2012, Dr Shipley took up her Lectureship (now Reader) position within the Biomechanical Engineering Group at UCL Mechanical Engineering, where she now leads an interdisciplinary research group on the development and application of mathematical models in medicine. In May 2017, she established the UCL Centre for Nerve Engineering with Dr James Phillips (UCL School of Pharmacy).

In 2018, Dr Shipley took on the roles of Vice Dean for Health within the UCL Faculty of Engineering Sciences and also Director of the UCL Institute of Healthcare Engineering. In these roles, she coordinates interdisciplinary research activities within healthcare engineering across Engineering, SLMS and the UCL Partner Hospitals at UCL.