Abstract: A grate assembly for a furnace for incinerating material comprises rows of moving grate bars which are arranged between rows of stationary grate bars and which are individually driven by drives arranged exteriorly of a combustion zone located beneath the rows of grate bars. Interposed between the grate bars and the drive are a lever system including a swivel lever fastened to a torsion shaft and a slide guide attachment for effecting approximately rectilinear movement of the moving grate bars. The torsion shaft is supported on sidewalls of the combustion zone and is rotatable and slideable by means of a bearing support which pivots about a shaft. Due to the approximately rectilinear movement and the optional, individual adjustment of the movement of adjacent moving rows of grate bars, the incineration behaviour of the material may be taken into consideration to a large extent and the drives may be easily maintained since they are readily accessible.