A new technology for processing rare-metal raw materials is reported, based on their decomposition using weakly acidic solutions rather than the concentrated acid solutions typically employed. Effective decomposition of the raw material by weakly acidic solutions is achieved through the continuous shifting of equilibrium resulting from the sorption-based removal of metal cations released into the acidic solution. The technology comprises the following main operations: acid decomposition of the raw material; desorption of metals from the sulfonic cation exchanger; regeneration of the sorbent; processing of the eluates to recover the metals and regenerate the desorbate; and disposal of the mother liquors. The physicochemical nature of the processes employed is discussed. Advantages of the proposed technology: high degree of comprehensive raw material utilization; minimal reagent consumption; energy efficiency; minimal harmful emissions into the gas phase; elimination of liquid waste generation; significant reduction in the volume of solid waste produced; and the possibility of using less expensive materials for equipment fabrication. It has been suggested that this approach could prove promising for the processing of non-ferrous metal sulfide concentrates and a number of other types of raw materials.