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We propose an iterative method for solution of a coupled acoustic fluid-solid interaction model. Assuming harmonic excitation in time, we use the pressure-displacement formulation of the acousto-elastic problem. The fluid is assumed to be ideal inviscid compressible medium governed by a wave equation for the acoustic pressure. The linear isotropic elastic structure is described by elasto-dynamic equations for the displacement field. We impose kinematic and dynamic conditions at the interface: The fluid particles velocity matches the velocity of the solid, and the balance of normal stresses holds. In the proposed iterative method, the fluid and solid subproblems are solved alternatingly, taking into account the interface conditions.  The convergence of the iterative algorithm is demonstrated numerically for fluid-solid structures with different periodic, as well as random interfaces. The algorithm is applied for comparison of acoustic properties of fluid-solid structures depending on the geometry of the rough interface.