Although many materials are used under extreme conditions, the effects of stress and strain are often neglected in material studies, especially when studying the solubility or calculating the diffusivity of substitutional or interstitial species. In this work, a general method based on firstprinciples calculations and elasticity theory in fcc systems is presented to fill this gap. The case of hydrogen in aluminum is investigated in detail as an application sample by comparing results from the density functional theory (DFT) and the elasticity theory. Additional systems, Ni, Cu and Pd, are also examined for hydrogen but in the framework of the elasticity theory only. Different types of stresses, i.e. hydrostatic, multi-axial and shear stress, are investigated for comparison purposes. The symmetry break induced by the loading is analyzed at the atomic scale by calculating the jump rates, at macroscopic scale from computed diffusion coefficients. Equations of diffusion are developed for each loading. Results show that the effect of loading on atomic parameters-insertion energies, energy barriers, etc.-can be accurately captured by the elasticity theory in terms of elementary parameters calculated using the DFT. Results show that the effect of stress is weak in the case of hydrogen.