An algorithm, based on Prony approach, for identification of the relaxation modulus of linear viscoelastic materials described by Maxwell model is presented. It is proved, that if the real relaxation modulus is four-element Maxwell and the measurements are not corrupted by noise, then the identifiability of the real parameters of the relaxation modulus is guaranteed. It is also proved that all the computational tasks solved in the identification scheme are well-posed in the Hadamard sense. Next the necessary and sufficient conditions for the applicability of the algorithm to identifying the four-parameter Maxwell models are derived. The effectiveness of the method is demonstrated through the computation of the relaxation function of the beet sugar root samples in the state of the uniaxial strain. The second example using Lanczos data is also enclosed.

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