Alkaline earth metals, Calcium and Strontium, are soft materials with a stable fcc crystal structure. In this work we have applied the Naval Research Laboratory Tight-Binding (NRL-TB) method to these materials using total energies and energy bands inputs generated by the Linearized Augmented Plane Wave (LAPW) method using the Generalized Gradient Approximation (GGA) for treatment of exchange and correlation. Accurate TB Hamiltonians have been obtained for Ca and Sr that fit very well the LAPW results of the fcc, bcc and sc structures for the total energy and band structure. Also, properties that were not fitted including elastic constants and phonon frequencies reproduce well the measured values, as well as producing total energies for the evaluation of structural differences. In addition, our model is successful in performing molecular dynamics (MD) simulations to derive quantities such as mean-squared displacements, vacancy formation energies and thermal expansion coefficients. Finally, we have shown that Sr which is known to have semi-metallic behavior can be turned into a semiconductor (possibly a topological insulator) upon applying spin-orbit interaction.