•Ab initio calculation of the surface relaxation of metals.•Surface energy and surface stress of transition metals.•Surface energy and surface stress of simple metals and light actinides. We investigated surface properties of metals by performing first-principles calculations. A systematic database was established for the surface relaxation, surface energy (γ), and surface stress (τ) for metallic elements in the periodic table. The surfaces were modeled by multi-layered slab structures along the direction of low-index surfaces. The surface energy γ of simple metals decreases as the atomic number increases in a given group, while the surface stress τ has its minimum in the middle. The transition metal series show parabolic trends for both γ and τ with a dip in the middle. The dip occurs at half-band filling due to a long-range Friedel oscillation of the surface charge density, which induces a strong stability to the Peierls-like transition. In addition, due to magnetic effects, the dips in the 3d metal series are shallower and deeper for γ and τ, respectively, than those of the 4d and 5d metals. The surface stress of the transition metals is typically positive, only Cr and Mn have a negative τ for the (100) surface facet, indicating that they are under compression. The light actinides have an increasing γ trend according to the atomic number. The present work provides a useful and consistent database for the theoretical modelling of surface phenomena. Display omitted