Because of its substantial c/a ratio, Zn has proven to be a problematic element to model using semi-empirical classical potentials. It has been shown, in particular, that for the modified embedded atom method (MEAM), a potential cannot simultaneously have an hcp ground state and c/a ratio greater than ideal. However, as an alloying element, practical Zn potentials can be generated by relaxing the condition that hcp be the lowest energy structure. A MEAM Zn potential is developed, which gives accurate material properties for the pure state and a MEAM ternary potential for the Mg-Al–Zn system, which will allow the atomistic modeling of a broad class of alloys containing Zn. Zn's effects in simple Mg–Zn results for this potential verifies the accuracy for the new potential in these systems.