High entropy alloys (HEAs) have attracted a great deal of attention. The fundamental theory and computational modeling of HEAs is still not fully developed. We propose a new approach based on building relatively large supercells of HEAs, and calculate their electronic structure and bonding to provide critical parameters, the total bond order density (TBOD) and the partial bond order density (PBOD). They avoid the use of a pure geometric description and implicitly include the entropy effect by virtual random distribution of atoms. Results from the DFT calculations on 13 bio-compatible HEAs (TiNbTaV, TiNbTaZr, TiNbTaZrMo, HfNbTaV, NbTaTiVZr, TiZrHfNbTa, TiHfNbTa, TiZrHfTa, TiZrHfNb, TiZrNbHfTa, ZrNbMoHfTa, TiZrNbMoHf, and TiNbMoHfTa) with supercells of 250 atoms in the cubic BCC lattice are presented. The calculated elastic and mechanical properties are in good agreement with the experimental data and correlate with the TBOD. For TiNbTaZrMo, introduction of porosity leads to a significant reduction in the Young’s modulus.