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Modelling of sound propagation in porous media generally requires the knowledge of several transport properties of the materials. In this study, a three-parameter analytical model that links microstructure properties of sintered metal fibre materials and non-acoustical parameters of the JCAL model is used and modified, and two heuristic approaches based on the established model for inverse acoustic characterisation of fibrous metal felts are developed. The geometric microstructure of sintered fibrous metals is simplified to derive the relationship between pores and fibre diameters. The new set of transport parameters in the modified three-parameter model can cover two controllable parameters during the fabrication process of fibrous metals. With two known transport parameters, six sintered specimens are characterised using a deterministic algorithm, and a satisfactory result is achieved in fitting the normalised surface impedance measured by an acoustic measurement system. Moreover, the forward evaluation shows that our modified three-parameter theoretical model is capable of yielding accurate results for the sintered metal fibre materials. A numerical investigation of the complete inverse acoustic characterisation of fibrous metals by a global non-deterministic algorithm indicates that inversion from two porous material properties is preferable to the normalised surface impedance.