The mass transport in the presence of stress, electrical, mechanical and chemical potential gradients in multicomponent solid solution is analyzed. The method bases on the Darken concept and the calorimetric equation of state. We effectively coupled the conservation of the mass (continuity equations), energy, momentum and Gauss equations. The diffusion fluxes of the components are given by the Nernst-Planck formulae and take into account the electro-chemical and mechanical potentials. We simulate the deformation field during the diffusion caused by the gradients of the chemical potential of all elements in non-ideal Fe-Cu-Ni alloy. The simulations show that the model is compatible with experimental results, and can be effectively used for modelling the energy, momentum and mass transport problems in compressible multicomponent solid solutions. The numerical problems and methods of solution are presented.