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Nowadays, rolling resistance sits at the core of tyre development goals because of its considerable effect on the car’s fuel economy. In contrast to the experimental method, the finite element (FE) method offers an inexpensive and efficient estimation technique. However, the FE technique is yet to be a fully developed product particularly for rolling-resistance estimation. An assessment is conducted to study the role of material viscoelasticity representation in FE, in linear and non-linear forms, through the use of Prony series and parallel rheological framework (PRF) models, respectively, on the tyre’s rolling-resistance calculation and its accuracy. A unique approach was introduced to estimate the rolling resistance according to the tyre’s hysteresis energy coefficient.