This paper discusses the effect of stress on the solubility and diffusivity of vacancies using the elasticity theory of point defects. To support the discussion, results are compared with DFT calculations to verify model accuracy. The particular case of vacancies in aluminum is discussed in detail (DFT-elasticity), while three other metallic fcc systems -- Ni, Cu and Pd -- are discussed through the elasticity approach only. Different types of loading were considered: hydrostatic, multi-axial and shear stresses. In the case of a uni-axial loading, two different directions were investigated: the first along a main crystallographic direction, i.e. [001], and the second perpendicular to the dense plane (111). In order to quantify the effect of stress on diffusivity, the diffusion coefficient of each configuration was expressed for further calculations. By analyzing the symmetry break during the loading process, non-equivalent atomic jumps were identified and diffusion equations obtained. A multi-physic approach was carried out by combining first-principles calculations, to study atomic-scale processes, and a multi-state formalism, to obtain exact diffusion equations. Results show that elasticity accurately captures the effects of stress on vacancy diffusion and solubility and an application method is presented.