In this work, we report a preliminary study, based on molecular dynamics simulations, about 3D carbon nanotube networks that could be formed inside the beta zeolites. We investigated their structural stability and mechanical properties. Our results show that from all possible carbon nanotubes that can be embedded inside the channels of the beta zeolite, the one with chirality (6,0) is the most stable. Using the carbon nanotube (6,0), it is possible to build 3D structures with both all (higher density) and only partially (lower density) filled zeolite channels. Under tensile uniaxial force, the 3D low-density carbon nanotube networks are anisotropic and can be stretched along the direction in which all nanotubes are perpendicular up to 130% of strain without fracture. Also, the porosity and network stiffness can be tuned depending on the amount of carbon nanotubes filling the channels of the zeolites.