To date, the examination of surface energy and surface layer relaxation has been the subject of several experimental and simulation works, whereas evaluation of surface residual stresses and surface elastic constants has received very little attention. In addition to the fundamental importance of these properties in the understanding of such phenomena as crystal equilibrium shape, surface roughening and segregation, they are also crucial for use in the theoretical studies based on continuum theory of elastic material surfaces. This work focuses on developing a theoretical approach for the calculations of the surface residual stress and surface elastic constants for (100) planes of fcc crystals. This is achieved through inter-relating the corresponding energies obtained from ab initio DFT calculations and from surface elasticity theory which deals with energetic material surfaces enclosing a classical simple elastic bulk material. Moreover, surface layer relaxations and surface energies associated with the (100) planes of Al, Ag, Ni, Pt, and Cu fcc crystals are evaluated using ab initio DFT calculations and compared with the available theoretical and experimental results.