The interaction between thin structures and incompressible Newtonian fluids is ubiquitous both in nature and in industrial applications. In this paper we present an isogeometric formulation of such problems which exploits a boundary integral formulation of Stokes equations to model the surrounding flow, and a non linear Kirchhoff–Love shell theory to model the elastic behavior of the structure. We propose three different coupling strategies: a monolithic, fully implicit coupling, a staggered, elasticity driven coupling, and a novel semi-implicit coupling, where the effect of the surrounding flow is incorporated in the non-linear terms of the solid solver through its damping characteristics. The novel semi-implicit approach is then used to demonstrate the power and robustness of our method, which fits ideally in the isogeometric paradigm, by exploiting only the boundary representation (B-Rep) of the thin structure middle surface.