The invention relates to a screen tensioning system having a mesh screen and a U-shaped channel that engages an edge of the mesh screen. A clamp engages the U-shaped channel and the mesh screen. A frame having a substantially H-shaped cross section, wherein parallel side members converge to define a longitudinal slot permit the mesh screen to extend through the longitudinal slot, yet the clamp remains secured within the frame. A plurality of fasteners secure the clamp to the frame and are tightened to apply varying degrees of local tension to the screen. Preferably, no fasteners are used to secure the screen to the clamp.