The recently discovered carbon nanotube-based super-nanotubes (SNTs), super-graphene (SG) and super-square (SS) are modeled using the equivalent beam concept (EBC). By substituting carbon nanotubes with elastic beams of identical mechanical behavior, the atomic lattice is simulated with the classical strut-based lattice, thus enabling continuum modeling using finite elements. Young's modulus, failure stress and strain of the SNTs are derived and compared against results from molecular-structural mechanics and molecular dynamics methods found in the literature. In general, a good agreement is achieved; occurred deviation is mainly due to the behavior of the nanotube Y-junctions which are omitted by the EBC. Parametric studies conducted reveal an appreciable influence of the SNT radius and chirality on the mechanical properties of the SNTs. In-plane elastic moduli of the SG and SS are also derived in regard of lattice size and arm-tubes' diameter. Most important finding is that the increase of the armtubes' diameter increases the elastic modulus of the SG and decreases that of the SS significantly. This contradictory effect is explained in terms of mechanics of load-transfer in the lattices. For all super-structures, extreme failure strains (18-76%), indicatory of their superior flexibility, are predicted. All simulations were performed under slight computational times since, in essence, beam FE models had to be solved. The inference drawn from the findings of the paper is that the EBC shows a potentiality in modeling CNT-based nanostructures owing mainly to its computational ease.