This paper deals with fluid–structure interaction analysis of an hexagonal rod enclosed in a narrow viscous gap. A new analytical solution for a two-dimensional (2D) cylindrical case is derived and described. A numerical solution of 2D Navier–Stokes equations coupled with a harmonic structure model is applied to both cylindrical and prism geometries. The comparison between the numerical tool and the analytical solution is discussed and a method to apply the analytical solution to the hexagonal case is proposed. An original definition of the added mass and damping based on an energetic approach is provided avoiding the dependence from the geometry and the type of forcing (free or forced vibration). An experimental facility is provided accounting for an hexagonal prism vibrating within a 7 mm enclosure. Free vibration experiments in water allow assessing the added mass and added damping effect on the modal parameters. The fluid flow is affected by a three-dimensional (3D) effect—named down-strokes flow—at the top and the base of the assembly because of free surface and stocky geometry. This produces a higher frequency than the 2D theoretical value given both by the analytical solution and the numerical simulation. A geometry-based correction factor is suggested to taken into account in the 2D numerical simulation the 3D effect. Velocity measured within the gap provides further insight on this phenomenon and agrees well with the prediction of the transposed cylindrical analytical model.