The magnetic responses of granular (NdBa2Cu3O7-x and YBa2Cu3O7-x) and monolithic (PbIn) superconducting plates, cooled in a fixed magnetic field H-z parallel to their plane and, later, subjected to cycles of a transverse magnetic field H-y with an amplitude H-y,H-max > H-z, are investigated both experimentally and theoretically. Magnetization curves, generated as H-y with H-z constant applied and of the order of the full penetration field H-p, are interpreted by employing two competing models (the double critical-state model and the two-velocity hydrodynamic model) for describing flux-line cutting effects on the magnetic behaviour of superconductors. Both models qualitatively and semi-quantitatively reproduce the experimental curves. Unlike the double critical-state model, the two-velocity hydrodynamic approach predicts the appearance of zones with homogeneous magnitude of the magnetic induction B at relatively small values of H-y as \H-y\ is increased. However the effect of these zones is not appreciable since they disappear when \H-y\ reaches a sufficiently large value: \H-y\ greater than or similar to H-z approximate to H-p.