Penetration of magnetic flux into type-II superconducting Nb strips is observed by a flux jump readout technique. To investigate the effect of the geometry, strips of different width are subjected to an increasing perpendicular magnetic field. We demonstrate that conventional geometrical barrier models cannot account for the onset of the flux migration into the strip volume. The migration starts for a local magnetic field at the strip equator higher than H c1 , allowing the irreversible penetration of the mixed state on the edges. The flux entry consists of flux bundles, each of them containing several hundreds of flux quanta. ͓S0163-1829͑99͒02134-7͔