The invention discloses a mounting device with an elastic hook and a construction method for hanging and combining building stone or ceramic tiles with mastic. The mounting device comprises a U-shaped or similarly U shaped elastic hook and an elastic hook shank, and the U-shaped or similarly U shaped elastic hook comprises two elastic edges elastically stretching out and arc portions integrated with the two elastic edges. The mounting device is characterized in that one end of the elastic hook shank is connected or integrated with one elastically stretching out elastic edge of the U-shaped or similarly U shaped elastic hook through a bent-out transverse elastic rod, the elastic hook shank is perpendicular or approximately perpendicular to the U-shaped or similarly U shaped elastic hook, a barb-type slant hook is connected or integrated to the outer end of the elastic hook shank, and an arc inward bend is formed at the outer end of the elastic hook shank and the inner end of the slant hook. By means of the elastic hook shank and the barb-type slant hook at the front end of the elastic hook shank, a veneer is reliably connected with a main wall through mastic posts cladding the elastic hook shanks, the veneer is permanently resistant to shedding, the construction method is simple, and construction quality is improved.