The present invention relates to a method and an apparatus for separating a suspension into a concentrate and a filtrate by means of cross-flow filtration. The suspension is introduced into a suspension chamber with a plurality of chamber-shaped modules arranged in series, in each of which an annular separating element with a separating surface is provided, in each module at least one stirring mechanism with radially arranged stirring elements In the suspension chamber, a movement is made above the separating surface at a small distance relative to the separating surface, so that in the gap between the stirring mechanism and the separating surface a directional flow is generated transversely to the separating surface. A pressure difference is set between the suspension chamber and the filtrate chamber for filtration, and the filtrate is led out through the filtrate line, and the filtrate passes through the separation element due to the pressure difference, and the suspension remaining in the suspension chamber is concentrated into a concentrate, which is discharged from the suspension chamber through the outlet elicited in. Using a sieve as the separation element, the average pore size of the sieve is larger than the average particle size of the solids in the suspension, on which the permeable target particle layer is filtered in a targeted manner, allowing it to be used for separating particles or producing a pure filtrate.