Hyperbolic metamaterials in which waves can only propagate through the radial direction have achieved much attention these days due to their capability of sub-wavelength resolution. In this work, the realization and optimization of hyperbolic elastic metamaterials are mainly studied. To obtain a new hyperbolic elastic metamaterial, a specially-engineered mass-spring system is introduced. Based on the mass-spring system, the hyperbolic elastic metamaterials are proposed and realized. In addition, the sub-wavelength resolution of the proposed hyperbolic elastic metamaterial is verified by ultrasonic elastic wave experiments. For the experiments, specially-designed magnetostrictive patch transducers are developed to realize two sub-wavelength elastic wave sources. Furthermore, the proposed hyperbolic elastic metamaterial is optimized to maximize its operating frequency ranges by the topology optimization method.