First-principles full-potential all-electron total-energy calculations on a seven-layer Mo(001) slab have found the equilibrium state of the slab and the energies of nearby states produced by isotropic two-dimensional (epitaxial) strain. In the slab equilibrium state, the in-plane lattice constant contracts 1.7% and the out-of-plane lattice constant contracts 0.7% from bulk values. The energy differences of these nearby states strained from equilibrium have been fitted to a composite elastic model of the slab which has two surface regions and a bulk region, each with three elastic parameters. The parameters of the surface regions determined by fitting the energy differences permit evaluation of the surface stress as 5.28 m Ry/bohr2 = 4.11 J/m². The surface region material is found to be less stiff than the bulk.