The theory of large deformations is used to construct exact solutions of a sequence of onedimensional boundary-value problems of the occurrence, development, and subsequent deceleration of viscometric flow of an elastoviscoplastic incompressible material located in the gap between rotating rigid coaxial cylindrical surfaces. In the quasistatic approximation allowing for slip of the material on its solid boundaries, the flow initiation conditions in the deformed material and the laws of motion of the boundary surfaces of the flow of this material both during its development and deceleration are determined. The parameters of the stress-strain states in the regions of reversible deformation and flow in all stages of the process, including the cessation of the flow and the complete unloading by rotation of the solid boundary in the opposite direction, are calculated.Viscosity of structural materials can be measured in viscometric experiments. The results of such tests are commonly processed using the exact solution of the corresponding model boundary-value problem. In the mechanics of viscous and viscoplastic media, such solutions are classical [1][2][3][4]. In the case of structural materials or elastic fluids, where the elastic properties of the test material cannot be ignored, the problems of viscometric flows are greatly complicated. In the flow regions of these materials, deformation cannot be considered small, and, therefore, the simplest mathematical model adequate to viscometric experiment is the model of large deformations of media with elastic, viscous, and plastic properties. A large number of geometrically closed and thermodynamically consistent mathematical models of plastic flow taking into account large elastoplastic deformation has been developed (see, e.g., [5][6][7][8][9][10][11]).When using these models in formulating and solving the problems of plastic flow, along with significant nonlinearity of boundary-value problems, a problem arises due to the motion of elastoplastic boundaries in the deformable medium during both active loading and unloading. The location and laws of motion of boundary surfaces at which deformations on the opposite sides are described by different systems of model equations are determined only in the process of solving the problem. Therefore, at present, a small number of exact solutions of problems of elastoplastic deformation have been obtained [12][13][14][15]. An exact solution of a problem modeling viscometric material flow in the gap between rigid cylindrical surfaces was constructed in [14] using the no-slip condition on the contact surface of the test material with rigid cylindrical surfaces. However, in experiments, it is difficult to achieve rigid contact of the test material with both the inner and outer rotating cylinders. Often, in

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This paper considers a deformation process of an incompressible elastoviscoplastic material placed between two coaxial rigid cylinders. The material is deformed when the internal cylinder rotates around its axis while the external one is fixed. The adhesion conditions are set on both boundary surfaces. The theory of large elastoviscoplastic deformations is used to solve the problem. The mathematical model is constructed in cylindrical coordinates.