A horse shoe has an upper with independent side walls that conform to the shape of the hoof. The upper includes a toe clip, two side tabs in the front half and two side walls in the rear half of the shoe, preferably all integral with a polymeric horseshoe with heel portions defining a gap. A cantilevered resilient bridge connects the heel portions, thus providing a spring-like structure tying the heel portions together. The top surface of the horseshoe has a grid of interconnected recesses and the upper has lateral perforations adapted to receive glue material. The shoe is fitted to the hoof by lining the surfaces of the upper and the horseshoe with glue and holding the shoe in place while the glue hardens, thereby securing the shoe to the hoof. Alternatively, the shoe is nailed on the hoof like a conventional horseshoe after removing the side walls.