Waste that contains fibers and combustible material is slushed in a continuous-operation high-consistency pulper (10) to suspend in water the fibers contained in the waste. From the pulper (10) are discharged substantially continuously a fiber suspension (P₁) through a screen plate; and non-defibrable material (R₁) by means of a mechanical transfer device (22). The fiber suspension (P₁) is sorted and cleaned for use as raw material in paper or board. The non-defibrable material (R₁) and the rejects (R₂-R₄) separated from the fiber suspension (P₁) in the sorting and cleaning stages are used as fuel in energy production and/or utilized as raw material.