Lightweight metal matrix composites containing a skeleton structure of titanium, titanium aluminide, or Ti-based alloy are manufactured by low temperature infiltration with molten Mg-based alloy or Mg-Al alloy at 450-750° C., with molten In, Pb, or Sn at 300-450° C., or with molten Ag and Cu at 900-1100° C. The skeleton structure with a density of 25-35% is produced by loose sintering of Ti or Ti-based alloy powders. A primary deformation of the Ti skeleton structure before the infiltration is carried out by cold or hot rolling or forging to obtain a porous flat or shaped preform with a porosity <50% and pores drawn out in one direction such as the direction of future rolling of the composite plate. A secondary deformation of the infiltrated preform is carried out by multistage cold, or especially hot rolling, to refine the microstructure of the infiltrated skeleton structure and transform it into the textured microstructure strengthened by intermetallic phases such as TiAl, Ti3Al, and TiAl3. Subsequent re-sintering or diffusion annealing form a fully dense final structure of the resulting material having improved mechanical properties. The molten Mg-based infiltrate is alloyed with Al, Si, Zr, Nb, and/or V with the addition of TiB2, SiC, and Si3N4 sub-micron particles as infiltration promoters. The molten Ag- or Cu-based infiltrate can be alloyed with elements depressing its melting point. The method allows for control of the microstructure of composite materials by changing parameters of deformation, infiltration, and heat treatment. The method is suitable for the manufacture of flat or shaped metal matrix composites having improved ductility, such as lightweight bulletproof plates and sheets for aircraft and automotive applications, composite electrodes, heat-sinking lightweight electronic substrates, sporting goods such as helmets, golf clubs, sole plates, crown plates, etc.