In this project, we have designed a new type of flexible surface, which we call a tensegrity fabric, and simulated the interaction of this flexible surface with a near-wall turbulent flow. The fabric is constructed by weaving together both members in tension (tendons) and members in compression (bars) to form a plate-class tensegrity structure, then covering this discrete flexible structure with a continuous flexible membrane. We have modeled the flow/structure interaction by coupling a spectral Direct Numerical Simulation (DNS) code resolving the (continuous) turbulent flow system and an efficient structural dynamics code which simulates direclty the motion of the (discrete) extensive, small-scale, and interconnected tensegrity structure. The structural dynamics code used was developed by Prof. Robert Skelton's lab at UC San Diego. An immersed boundary method is used to capture the effect of the moving boundary in the DNS, and a simple tessellation strategy is used to lump the distributed fluid forces (skin friction and pressure) acting on the membrane onto the nearby nodes of the tensegrity structure. Our ultimate goal is to use this new simulation tool to optimize the design of the tensegrity structure (specifically, the orientation, stiffness, mass, and damping of each of the individual tendons and bars in the unit cell upon which the tensegrity structure is based). Our objective in this optimization is to tune the compliance properties of the fabric in such a way as to reduce the skin-friction drag induced at teh flow/structure interface by weakening the vortices near the wall in the overlying turbulent flow.