Theoretical quantum calculations have been carried out for two new ibuprofen and naproxen based Non Steroid Anti inflammatory Drug candidates. DFT (Density Functional Theory) calculations of molecules have been carried out with a general quantum chemistry software package GAMESS (the General Atomic and Molecular Electronic Structure System). Both molecules have been optimised successfully, and IR (Infra Red) spectra have been obtained via vibrational HESSIAN analyses. The frontier orbitals, HOMO (the Highest Occupied Molecular Orbital) and LUMO (the Lowest Unoccupied Molecular Orbital) have been obtained, and also molecular dynamic descriptors, such as chemical hardness, electronegativity and electrophilicity have been calculated for both molecules. Electrostatic potentials, total molecular electron densities also have been calculated for optimised molecules. All the result has been represented comparatively for both molecules.Keywords: Ibuprofen, Naproxen, DFT, GAMESS.DOI: 10.7176/JHMN/78-0