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Many biological systems involve flexible structures moving in viscoelastic fluids, such as cilia transport in the lungs, microorganism motility in mucus, and blood clot formation. This talk will describe ongoing work to study such systems with the immersed boundary (IB) method. Initially developed to study heart valves, the IB method has been used to study numerous types of fluid-structure interaction problems. Although the IB method has previously been used in conjunction with viscoelastic fluid models, a detailed analysis of the method in this regime is lacking. Common viscoelastic fluid models are known to exhibit instabilities and fine boundary layers in the types of flow regimes often found in fluid-structure interaction models. This talk will address the accuracy of the method and discuss some of the challenges of using the IB method with viscoelastic fluid models. Finally, this talk will show results from application of the IB method to different model problems, such as twirling flagella and blood clotting