We aim to improve the calculation of the Mg I line profiles in benchmark stars and to assess the impact of the new quantum mechanical calculations of inelastic collisions with hydrogen. The method is based on the non-Local Thermodynamic Equilibrium (NLTE) line formation using updated atomic data for a simple model atom of Mg I. Focus on the formation of the Mg I b triplet lines at 5167, 5172 and 5183 Å is presented for the Sun, Arcturus, HD 84937 (metal-poor dwarf) and HD 122563 (metal-poor giant). This study is preliminary and essentially tests the new atomic data. In this context, we show that NLTE effects are smaller for this triplet when quantum mechanical H collisions are included compared with the use of the semi-classical Drawin's formula.