AbstractThe coupling of lightweight and often thin‐walled structures to fluids in an incompressible regime is a recurring theme in biomechanics. There are many fluid–structure interaction (FSI) solution schemes to address these kinds of problem, each one with its costs and benefits. Here, we attempt a comparison of the most important FSI schemes in the context of biomechanical problems, that is a comparison of different fixed‐point schemes and a block preconditioned monolithic scheme. The emphasis of this study is on the numerical behavior of these FSI schemes to gain an understanding of their effectiveness in comparison with each other. To this end a simplified benchmark problem is studied to show its applicability for more involved biomechanical problems. Two such examples with patient‐specific geometries are also discussed. The monolithic scheme proved to be much more efficient than the partitioned schemes in biomechanical problems. Copyright © 2009 John Wiley & Sons, Ltd.