An unsteady Reynolds-averaged Navier–Stokes (URANS) model coupled with an immersed-body method is used to model fluid-structure interaction (FSI) for moderate Reynolds number flows. Particular attention is paid to the application of suitable flow boundary conditions with the immersed-body method. This model couples a combined finite-discrete element solid model and a finite element fluid model with the standard k−ε model. A thin shell mesh surrounding the solid surface is first used as a delta function to apply the interface boundary conditions for both the URANS model and the momentum equation. In order to reduce the computational cost, a log-law wall function is used within this thin shell to resolve the flow near the solid wall. To improve the accuracy of the wall function, a novel shell mesh external-surface intersection approach is introduced to identify sharp solid-fluid interfaces. More importantly, an unstructured anisotropic mesh adaptivity is used to refine the mesh according to the interface and the velocity, which improves the accuracy of this immersed-body URANS model with use of a limited number of fluid cells. This immersed-body URANS method is validated by several test cases and results are in good agreement with both experimental and numerical data from the literature.