The ultimate goal of this work is to allow a surgeon to simulate surgery within the operating theatre in real time using readily-available computing facilities, and to visualise the results immediately. Thus a surgeon would be able to assess the implications of each stage of a surgical procedure, explore possible alternative courses of action or solutions to problems that arise, as events unfold during a complex operation. Achieving this goal requires the development of an easily-manipulated computational grid, allowing the user to zoom-in or out of areas of interest using a touch-screen, which would allow the fundamental equations which describe the biomechanical behaviour of the subject to be solved using the graphics processing unit (GPU) on an ordinary computer. The user should not require specialist knowledge in the field of computational biomechanics, hence the operation of such a system must be robust and reliable, and the results presented to the surgeon must be repeatable, consistent, and within guaranteed bounds of accuracy. Existing methods for computational biomechanics using the finite element method (FEM) have limitations that prevent their use in the operating theatre. This project will overcome these challenges by developing methods to automatically generate computational grids from medical images, and to deliver robust, accurate and reliable results in real-time on standard computer hardware. These new modelling and computing techniques can be used for surgical planning, virtual surgical training systems, and in Computer-Integrated Surgery Systems to improve clinical outcomes and the efficiency of health care delivery. This will assist collaborating teams from Australia and Luxembourg to become international leaders in computational biomechanics research and computer-assisted surgery. Computational mechanics has been extraordinarily successful in traditional engineering. This project will deliver some of the same benefits to the field of medicine, improving the clinical outcomes of surgery and increasing efficiency of health care delivery. The applications of the proposed modelling and computing techniques extend beyond biomechanics for medicine, to computational mechanics problems in e.g. engineering design, geomechanics and mining.The research proposed here centres around two visits of Prof. Miller in Luxembourg for which funding is sought: seven months in 2015 and five months in 2016. Nevertheless it must be understood that both Prof. Bordas and Prof. Miller lead research groups of 20+ postdoctoral fellows and PhD students and that therefore human resources available for this project go beyond the applicant and the invitee.