The techniques involved in designing a simple and transferable semi-empirical potential for numerical simulations of Li, Na, and K metals and alloys with a minimal fitting have been put forward. The embedded-atom method provides the most reliable and efficient semi-empirical atomic potentials used for various simulations. Here, this method is employed to study and theoretically reproduce some physical properties of materials, which are also gotten from the experiment and the ab initio calculations. To validate the suitability of this model, we optimally computed and reproduced the monovacancy formation energy and the elastic stiffness of these metals that comparably agree with the data from experiments. Additional properties like low index surface energies that were not used during fittings were computed. The obtained values reasonably agree with the data both from experiment and first principles. The little differences may be due to the inability to adequately determine the experimental values using Tyson’s estimation. Lastly, the six possible binary alloys of these metals were studied. Only two experimental sets of data are available at the moment for NaK and KNa, and our computed values are consistent with these data. Thus for a better and complete comparison, new experimental data are needed for other alloys.