We have studied, by quenched molecular dynamics (QMD) using a second-moment approximation (SMA) potential, the atomic relaxations and step interaction energies on Ni, Cu, Pt and Au vicinal surfaces for which steps run along the [1-10] direction. The results have been compared to anisotropic linear elasticity calculations (ALE). We show that steps are well described with a model of lines of force dipoles buried under the surface. The elastic interaction energies between steps obtained by SMA and ALE are in good agreement. This demonstrates that the elastic step interaction energy can be determined from the measurement of the atomic relaxations.