Solving the problem of large elastic-plastic deformation theory, the present paper addresses, involved two stages. We first derive the exact solution to the problem of slow strain growth in a cylindrical layer consisting of an incompressible elastic/viscoplastic material and experiencing viscometric motion subject to no-slip contact between the material and the rigid instrument's walls. Then a striking stick-slip transition at one of the material-instrument interfaces poses the problem of unloading dynamics. Stress jump at the boundary surface causes a shear cylindrical unloading shock wave, which advances into the material and interacts with the elastic-plastic boundary separating viscoplastic flow from reversible deformation region. To solve this dynamic problem the ray method for constructing approximate solutions is adjusted to the case of elastic/viscoplastic material.