An apparatus for concentrating a vegetable and/or fruit product has a concentration unit having a plurality of tubular membrane modules connected in series, a single-axis eccentric screw pump connected to its inlet for supplying the product and another single-axis eccentric screw pump connected to its outlet for discharging the product concentrated by reverse osmosis by the concentration unit. The product is supplied under a high-pressure condition such that the pressure at the inlet is within a specified range, and the apparatus is operated such that the pressure at the outlet is also within another specified range and the pressure difference between the inlet and the outlet be greater than a certain minimum pressure value.