Between the fatigue limit of solids and the surface stress an inherent relation is supposed. Using the simple quantum mechanical model of Kronig and Penney for the energy bands in solids and the model of Tamm for the electronic surface states, with analytical relations a close connection is demonstrated between the strength of solids and the quantities 'surface free energy' and 'surface stress'. Due to the electrocapillarity, it can be deduced an influence of electric fields on the strength of solids.