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The article presents a method for determining the parameters that define the cooperation of the elements in the axisymmetic connection. The connection, which constitutes a shaft cooperating with a sleeve, has been tested for reaction forces in the connection during shaft rotation in the static sleeve. The shaft was characterized by deliberately modelled roundness deviations in the form of ovality, triangularity and quadrangularity.  In addition, the research programme has taken into account the determination of the impact of tolerance of the outside diameter of the shaft. Determination of reaction forces has been carried out using the FEM software. The shaft has been modelled as a rigid element that rotates with a given rotational speed in the deformable sleeve. The conclusions present the impact of roundness deviation types and the tolerance value on reaction forces in the connection restraint. The method presented in the article can be used to predict the behaviour of the elements of axisymmetic connections under dynamic load, which can contribute to forecasting the durability of the connection.