Solution strengthening or softening is an effective way to enhance mechanical properties, especially in magnesium based alloys due to their inability to activate adequate non-basal deformation mechanisms at the room temperature. Hence, using first-principles calculations, the effects of several different alloying elements on the ideal shear resistance across various slip systems of Mg were investigated. The results reveal that the addition of a Ce or Zr solute atom decreases the ideal shear resistance (softening); whereas, the substitution of a Sn, Li or Zn atom increases the ideal shear resistance of Mg (strengthening). The dominant slip system in Mg was found to change from the basal partial (0001)[101¯0] to prismatic (101¯0)[112¯0] with the addition of a Ce or Zr solute atom; whereas, the addition of a Sn, Li or Zn solute atom had negligible effect on the plastic anisotropy. Furthermore, the electronic density of states and valence charge transfer, which provides a quantum mechanical insight into the underlying factors influencing the observed softening/strengthening behavior, was probed. For instance, the electronic density of states calculations show that the contribution from d states of Ce and Zr solute atoms decreases the electronic structure stability of their respective solid solution, thereby enhancing slip activities. In the end, theoretical analyses were performed and a shearability parameter was introduced to understand the implications of the observed variation in ideal shear resistance on the macroscopic behavior of Mg alloys. © 2018 Acta Materialia Inc.