A sub-frame structure of a motor vehicle includes a pair of side frame sections and a cross member section. The pair of side frame sections extend in the longitudinal direction of the vehicle at prescribed lateral spacing and include laterally inward bends in each section. The cross member section connects front ends of the side frame sections. The cross member section and end portions of the side frame sections connected to the cross member section are integrally formed of a deformed tube member. The remaining portions of the frame member sections including said bends are formed of a closed section member fabricated by joining a plurality of members at flanges.