The numerical simulation of deformable solids has many applications in fluid-solid interaction such as hydroelasticity and aeroelasticity. The greatest application is in medical engineering in which it will be possible to simulate the movement of tube like structures such as the oesophagus, intestines, bile duct, fallopian tube, uterus, ureter and blood vessels etc. However, the numerical simulation of the movement of individual blood cells in either a laminar or turbulent fluid flow is particularly difficult because it not only involves the correct modelling of the fluid flow but also the movement of the cells themselves which, in turn, requires the correct modelling of their dynamics, surface stresses and their surface deformations in response to these stresses. This project is aimed at investigating the deformation, movement and collision of deformable solids in laminar and turbulent flow. In order to do this it will be necessary to couple existing in-house discrete element and computational fluid dynamics codes. The boundaries of the solids will be allowed to deform under the pressures and stresses imposed on them by the surrounding fluid. Such a numerical scheme would also involve taking into account the possible collision of the cells and their ‘shielding’ and imbrication by other cells. The potential benefits of a code that could do this are enormous as it would be possible to investigate the exact cell movement mechanism, and lead to the design of better stents. A further project objective is to carry out simulations of peristaltic pumping by wavelike contractions which are fundamental biomechanical mechanisms for fluid and material transport and are used in the oesophagus, intestine, oviduct and ureter.