Vibratory screening machines that include stacked screening deck assemblies are provided. In some embodiments, at least one of the vibratory screening machines can include an outer frame, an inner frame connected to the outer frame, and a vibratory motor assembly secured to the inner frame for vibrating the inner frame. A plurality of screen deck assemblies can be attached to the inner frame in a stacked arrangement, each configured to receive replaceable screen assemblies. The screen assemblies can be secured to respective ones of the plurality of the screen deck assemblies by tensioning the screen assemblies in a direction that a material to be screened flows across the screen assemblies. An undersized material discharge assembly can be configured to receive materials that pass through the screen assemblies, and an oversized material discharge assembly can be configured to receive materials that pass over the screen assemblies.