This article addresses the interaction of two coaxial cylinders separated by a thin fluid layer. The cylinders are flexible, have a finite length, and are subject to a vibration mode of an Euler–Bernoulli beam. Assuming a narrow channel, an inviscid and linear theoretical approach is carried out, leading to a new simple and tractable analytical expression of the fluid forces. We show that the dimensionless form of this matrix reduces to a single coefficient whose properties (sign and variations) strongly depend on the boundary conditions, the wave number of the vibration modes, and the aspect ratio of the cylinders. All these properties are made explicit in our formulation, which applies to all classical types of boundary conditions. A numerical approach based on an arbitrary Lagrange–Eulerian method is also presented and successfully compared to the theoretical predictions.