This paper considers the fluid–structure interaction problem of two coaxial cylinders separated by a thin layer of fluid. The flexible inner cylinder is imposed a small amplitude harmonic displacement corresponding to a dry vibration mode of an Euler–Bernoulli beam, while the external cylinder is rigid. A new theoretical formulation based on the assumption of a narrow fluid annulus is derived to estimate the modal added-mass matrix of the vibrating cylinder. This formulation accounts for the finite length of the flexible cylinder, clearly highlights the effect of the aspect ratio of the vibrating cylinder on the structure of the added-mass matrix, and covers all types of classical boundary conditions in the same theory and can easily be implemented in any numerical computing environment. The diagonal coefficients of the added-mass matrix are shown to increase with the confinement, with the aspect ratio of the flexible cylinder, and are sensitive to the wave-number of the vibration mode. Also importantly, we show that the dry vibration modes generate off-diagonal coefficients that vanish for an infinitely long cylinder. Our theoretical observations are corroborated by an extensive set of CFD numerical simulations, covering all types of classical boundary conditions, different confinement configurations, and different aspect ratios of the vibrating cylinder. The results obtained are presented in graphical form, which can be directly applied in engineering applications.