We report the detection of fast (similar to 1000 km s(-1)), massive outflows of neutral gas observed - using the WSRT - as 21- cm H), Hi absorption against the strong radio continuum of seven radio sources. The neutral outflows occur, in at least somes cases, at kpc distance from the nucleus, and they are most likely driven by the interactions between the expanding radio jets and the gaseous medium enshrouding the central regions. We estimate that the associated mass outflow rates are up to similar to 50 M(circle dot)yr(-1), comparable ( although at the lower end of the distribution) to the outflow, rates found for starburst- driven superwinds in Ultra Luminous IR Galaxies ( ULIRG). This suggests that massive, jet- driven outflows of neutral gas in radio- loud AGN can have as large an impact on the evolution of the host galaxies as the outflows associated with starbursts. A radio- loud phase of the AGN is likely a relatively common, albeit short, phase in the life of many ( or even all) massive ellipticals. Jet- driven neutral outflows may represent one of the main feedback mechanisms in these galaxies.