The invention relates to a method of clarifying and/or thickening a solution containing solids i.e. a slurry, and the apparatus for accomplishing this. Using the method and apparatus of the present invention, the flocculant to be fed into the clarification and thickening equipment is mixed evenly and with a small shear force into the slurry in the feedwell of the apparatus. The feedwell is equipped with a mixing device. The slurry is taken onwards from the feedwell evenly into the clarification tank inside the underflow layer, which enables the separation of a clear overflow solution.