An analytical model for use in the inverse problem of estimating material properties of suspended fibres from ultrasonic attenuation has been developed. The ultrasound attenuation is derived theoretically from the energy losses arising when a plane wave is scattered and absorbed off an infinitely long, isotropic, viscoelastic cylinder. By neglecting thermal considerations and assuming low viscosity in the suspending fluid, we can make additional assumptions that provide us with a tractable set of equations that can be solved analytically. The model can then be to used in inverse methods of estimating material properties. We verify the model with experimentally obtained values of attenuation for saturated Nylon fibres. The experimental results from Nylon fibres show local peaks in the attenuation which are thought to be due to the resonant absorption at the eigenfrequencies of the fibres. The results of the experiments show that the model is sufficiently sensitive to detect differences in different types of Nylon. Applications for suspended fibre characterization can be found in the paper manufacturing industry.