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The article emphasizes the importance and necessity of studying the behavior of automobile tires during operation in the starting mode, from the beginning of driving on “cold” tires to stabilizing its temperature and internal pressure. During this period, the main performance characteristics of the tire can change in a relatively wide range. Therefore, the main focus was on the initial period of driving as the most dangerous from the point of view of predicting the behavior of automobile tires. This article presents the results of analyzing a car tire’s condition and behavior during the starting movement. Features of the main parameter for assessing the stiffness characteristics of the tires were investigated. The research was conducted under conditions of low ambient temperatures during the operation of automobile tires. A numerical-analytical approach was used to estimate the stiffness parameters. Simultaneously, the initial data required for a correct analysis were obtained from the experimental results in actual road conditions. The obtained results allow for providing recommendations on the peculiarities of the automobile tires’ operation under adverse conditions, such as low ambient temperatures.