In this work, we present an approach for solving fluid structure interaction problems by combining a non-linear structure solver with an incompressible fluid solver using immersed boundary method. The implementation of the sharpinterface immersed boundary method with the fluid solver is described. A structure solver with the ability to handle geometric nonlinearly is developed and tested with benchmark cases. The partitioned fluid-structure coupling algorithm with the strategy of enforcing boundary conditions at the fluid/structure interaction is given in detail. The fully coupled FSI approach is tested with the Turek and Hron fluid-structure interaction benchmark case. Both strong coupling and weak coupling algorithms are examined. Predictions from the current approach show good agreement with the results reported by other researchers. © Copyright 2016 by ASME.