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(copyright) 2022 Elsevier LtdWe present a method for computing fluid¿structure interaction problems for multi-body systems. The fluid flow equations are solved using a fractional-step method with the immersed boundary method proposed by Uhlmann (2005). The equations of the rigid bodies are solved using recursive algorithms proposed by Felis (2017). The two systems of equations are weakly coupled, so that the resulting method is cost-effective. The accuracy of the method is demonstrated by comparison with two- and three-dimensional cases from the literature: the flapping of a flexible airfoil, the self-propulsion of a plunging flexible plate, and the flapping of a flag in a free stream. As an illustration of the capabilities of the proposed method, two three-dimensional bio-inspired applications are presented: an extension to three dimensions of the plunging flexible plate and a simple model of spider ballooning.