Solute strengthening of twin dislocation motion along an existing twin boundary in Mg–X (X = Al, Zn) is investigated using a new Labusch-type weak pinning model. First, the View the MathML source(101¯2) twinning dislocation structure is computed using first-principles methods. Second, the interaction energies of Al and Zn solutes with the twin boundary and twin dislocation are computed. It is shown that the interaction energies of Zn solutes scale with the Al solute energies in proportion to the misfit volume plus an additional “chemical” interaction factor, demonstrating an efficient means for estimating the solute energies of other solutes. Third, the solute–dislocation interaction energies are used in a new Labusch-type model to predict the overall solute strengthening of the twinning dislocation. New features emerge in the application of the model to twinning because of the very small Burgers vector of the twin dislocation, leading to a new functional form for the dependence of the strengthening on concentration, temperature and strain rate. Fourth, application of the model leads to parameter-free predictions that agree well with available experimental data on various Mg–Al–Zn alloys. The predicted strengthening is not large, e.g. ≈10≈10 MPa for the AZ31 alloy at room temperature, but is larger than the strengthening of basal slip by the same solutes. Overall, this work demonstrates the ability of mechanistic theories to provide a quantitative understanding of alloying effects on deformation modes in Mg.