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A new approximate model of the tire rolling accounting for coupled longitudinal and lateral sliding as well as the spinning and the deformed state resulting in elastic forces is proposed. The main goal of this investigation consists in the construction of simple models with a few of degrees of freedom allowing one to implement them analytically in the engineering practice, primarily for the estimation of the rolling stability and for the prognosis of the instable rolling so-called “shimmy phenomenon” and to numerical simulation of the transient dynamics of rolling wheels with sliding effects. Such a model could become useful at the earlier stages of the engineering design when complex numerical models that are usually resource consuming.