Metamaterials are engineered materials with material properties which do not exist in nature. The major reason for the properties is result from structure rather than composition. Particularly, mechanical metamaterials have their distinct characteristics, such as negative bulk modulus or Poisson’s ratio, from mechanical properties. Here, we apply the concept of the mechanical metamaterial to triply periodic bicontinuous structures which have been researched as a promising candidate for 3D photonic crystals. Elastic properties should be measured to evaluate the prospect of mechanical metamaterials. We conduct simulations to evaluate Young’s modulus and shear modulus of triply periodic bicontinuous structures, such as simple cubic(P), diamond(D), and gyroid(G). Volume fraction and aspect ratio of unit cell are considered as shape determining parameters. Each ratio of the Young’s modulus to the shear modulus is compared to common materials in nature. Finally, we suggest that the simple cubic structure with low volume fraction and large aspect ratio has extremely high moduli ratio. Therefore it is suitable for the 3D mechanical metamaterial.