Abstract: In a vibratory screening apparatus, a withdrawable lower fine mesh screen assembly (17) has a screen unit (19) releasably mounted on a grid/frame structure (20). The screen unit (19) has a sheet (21) of mesh material bonded to a grate or lattice (22) of a yieldable material such as a hard rubber, and this lattice (22) and the edges of the mesh (21) are also fixed to relatively rigid side members (23) which are mutually free each from the others. In the structure (20), a rigid grate of support bars (26) supports the lattice (22) with a sliding contact interface, and a frame (28) incorporates pneumatically actuated tensioners (30) and clamps (34A, 34B) respectively for tensioning/locking the screen unit (19) and coupling the screen assembly to the vibratory structure. The tension in the screen unit (19) is adjustable whilst on the structure (20) by virtue of the yieldability of the lattice (22) and its sliding contact interface with the support bars (26).