A screen panel retainer assembly, that is utilizable with a vibrating separatory machine, is configured with a plurality of discrete, mushroom-shaped screen panel retainers. Each such retainer has a retainer head that is generally in the shape of a portion of a cylinder, such as a right cylinder. A shank connects each such retainer head to a suitable retainer bar. The retainer bar can be adapted to be attached either to screen stringer tubes of the vibrating separatory machine, or to underlying cross tubes and end cross tubes. The screen panels, which are to be secured to the vibrating separatory machine, have complementary shaped mushroom-shaped screen panel retainer head receiving chambers in their side surfaces. Two such panel edges define a whole chamber. The retainer heads are metal whereas the screen panel edges are resilient. The mushroom-shaped heads securely snap into their complementary chambers yet can be removed from those chambers when the screen panels have to be replaced.