A vibratory screening machine having opposite sides with a plurality of stationary aligned tensioning members mounted on one side and a plurality of nut actuated movable tensioning members mounted on the opposite side and a vibratory screening screen mounted on the stationary and movable tensioning members. The tensioning members have upstanding fingers which are received in apertures in the plates of the vibratory screen, and the edge portions of the vibratory screen include screening material which extends all of the way to the extreme edges of the supporting plate and the fingers are below the screening material. Also, the tensioning structure is mounted on the side walls of the vibratory screening machine below the vibratory screen.