Tensile tests on Al–Mn–Si ternary alloys show that a small amount of Si increases significantly the strength compared to Al–Mn binary alloys with the same concentration of Mn. This cannot be explained by classical theories for multi-element substitutional solid solution hardening under the assumption of no interaction between different alloying elements. A new simplified cluster strengthening model which addresses both the chemical and size misfit effects of atom dimers is proposed this work. The binding energies and misfit of dimers were estimated by first principles atomistic simulations. The prediction results of the model are reasonably consistent with the experimental results. It shows that the main strengthening contribution is due to the misfit of dimers.