Mechanical metamaterials that are engineered with sub-unit structures present unusual mechanical properties depending on the loading direction. Although they show promise, their practical utility has so far been somewhat limited because, to the best of our knowledge, no study about the potential of mechanical metamaterials made from sophisticatedly tailored sub-unit structures has been made. Here, we present a mechanical metamaterial whose mechanical properties can be systematically designed without changing its chemical composition or weight. We study the mechanical properties of triply periodic bicontinuous structures whose detailed sub-unit structure can be precisely fabricated using various sub-micron fabrication methods. Simulation results show that the effective wave velocity of the structures along with different directions can be designed to introduce the anisotropy of stiffness by changing a volume fraction and aspect ratio. The ratio of Young's modulus to shear modulus can be increased by up to at least 100, which is a 3500% increase over that of isotropic material (2.8, acrylonitrile butadiene styrene). Furthermore, Poisson's ratio of the constituent material changes the ratio while Young's modulus does not influence it. This study presents the promising potential of mechanical metamaterials for versatile industrial and biomedical applications.