Simulation of elastic filaments interacting with incompressible viscous fluid by the immersed boundary method Luoding Zhu Math Dept of IUPUI The Nature is rich in fluid flexible structure interaction problems. For instance, the insect flights and the motion of red blood cells in blood vessels. Because of the complex three-dimensional free moving deformable boundary and the coupled system of elasticity and hydrodynamics, the coupling interaction of viscous fluids and elastic structures is complicated and not well understood, even in a lower dimensional passive case -- a flexible filament immersed in a viscous fluid. It has become apparent that the immersed boundary (IB) method is a practical method for solving problems of this type. In this talk we will discuss the IB method (both mathematical formulation and numerical methods) and its current applications in simulation of a flexible fibre tethered at its center point in a flowing viscous fluid and interaction of elastic filaments with a 2D pulsatile flow.