A shock-absorbing or vibration-absorbing assembly includes a metal base and an elastic shock-absorbing or vibration-absorbing material secured to the metal base. A top surface of the metal base has at least one orifice extending from the top surface to at least one hollow chamber beneath the top surface. The hollow chamber occupies a planar area of the metal base parallel to the top surface that is larger than a planar area of the metal base that is occupied by the orifice at the top surface. The elastic material is secured to the metal base by the elastic material filling the orifice and the hollow chamber of the metal base and the elastic material filling a region above the top surface of the metal base that has a cross-sectional area parallel to the top surface of the metal base that is larger than the planar area of the metal base that is occupied by the orifice at the top surface of the metal base. The elastic material is secured to the metal base by placing the metal base against a mold having a hollow space to be filled with the elastic material. The elastic material is injected into the hollow chamber and orifice of the metal base and into the hollow space of the mold. The mold is removed from the metal base, so that the elastic material is secured to the metal base by the elastic material filling the orifice and the hollow chamber of the metal base and the elastic material filling a region above the top surface of the metal base that corresponds to the hollow space of the mold.