The present invention relates to a vertical low-pressure reactor with stirred tank for leaching polymetal minerals and concentrates of lead, copper, zinc, iron and/or the mixtures thereof, in a solid-gas-liquid three-phase suspension system. The low-pressure vertical reactor with stirred tank consists of: a cylindrical vertical container with three or four deflectors equidistantly distributed across the 360°; a stirring system made up of two impellers coupled to a rotary shaft, that provides adequate reaction and interaction of the metal species of interest; a space of the volume of the reactor, corresponding to 20% to 35% of the total volume of the container, located at the top of the reactor and which acts as a gas chamber that provides a continuous feed of oxygen; and a system of coils placed on the outside or inside surface of the reactor to ensure efficient heat-transfer reactions and controlled kinetics.