The invention is concerned with sets for mechanical processing, in particular refining, of suspended fibrous material as material to be treated in a refiner. A set comprises a die plate (2) which is configured as a perforated plate with receiving openings (12) in a predefined arrangement, into which blade-shaped processing elements (3) which protrude on the process side and are flowed onto by the fibrous material are inserted. Said blade-shaped processing elements (3) in each case have a plurality of base regions (10) which are spaced apart in the longitudinal extent, pass through the die plate (2) and project beyond the die plate (2) on the side which is remote from the process. In one design variant, at least some of the base regions (10) of the processing elements (3) reach into associated receiving grooves of an additional base plate (8) on the side (14) which is remote from the process. In one alternative embodiment, transverse stiffening elements (4) are provided which are arranged substantially orthogonally in the longitudinal direction of the processing elements in such a way that the transverse stiffening elements (4) stabilize the base regions (10) of the processing elements on the side which is remote from the process.