The suppression of the static magnetic moment M of a superconducting plate in the critical state by a sweeping magnetic field h⃗(t), applied perpendicularly to a dc magnetic field H→, has been studied experimentally and theoretically. For every quarter-period of a sweeping field h(t) of changing polarity with an amplitude h0, a noticeable decrease of M can be observed both for the paramagnetic and diamagnetic initial states even for small h0 compared to H. Numerical simulations within the framework of two existing theoretical approaches have been performed in order to study the evolution of the distribution of the magnetic induction and the suppression of the magnetic moment. It turns out that the Clem–Pérez-González double critical-state model describes this process qualitatively well in the first quarter-period for relatively high values of h0. A significant disagreement with the experimental data is observed for small values of the transverse magnetic field. On the other hand, the two-velocity hydrodynamic model provides an adequate explanation of the main features of the suppression of M for both paramagnetic and diamagnetic states and any values of h0.