The possibility of generation of the rotating sideways force on the wall by the kink modes is analytically investigated. The approach is basically the same as that developed earlier in (Mironov and Pustovitov 2017 Phys. Plasmas24 092508) for the locked modes, but now their rotation is allowed. Its main elements are ∂b/∂t ≠ 0 (described by the growth rate γ and angular rotation frequency ω of the magnetic perturbation b), resistive dissipation in the wall, and the requirement of zero sideways force on the plasma. These make the approach greatly different from those resulting in the so-called Noll's formula. The result is also different; it predicts a force an order of magnitude smaller. Nevertheless, such a force can be dangerous at the resonance frequency of the vacuum vessel. The derived relations show that the rotating force must be maximal at ωτw = O(1), where τw is the resistive wall time. For the faster modes it decreases roughly as ∼1/ω.