A belt press solid/liquid separation apparatus is provided for separating organic mixtures with substantial amounts of moisture to produce separated solids with solids content of 50-90% while retaining 99% of the incoming solids in the filter cake. Specifically, the invention incorporates a double-belt press apparatus with a non-permeable upper belt, a highly permeable lower belt, a wedge type zone with adjustable spring compression, and a means for re-screening belt press filtrate with either a single belt press or multiple belt presses configured as a multi-step cascade of belt presses.