We have studied the step–step interactions on the Pt(997) vicinal surface. Grazing incidence X-ray diffraction (GIXD) allowed us to measure the elastic atomic relaxations near the surface due to the steps. By means of the model of buried elastic dipoles, within the framework of anisotropic linear elasticity (ALE) calculations, the surface stress of Pt(111), and the elastic interaction between steps are deduced. The values so-obtained are compared to the values previously measured on the Pt(779) surface with the same technique. The comparison shows the strong influence of step geometry on step interactions.