The static and dynamical properties of NaF and NaCl at high pressures in both the B1 (NaCl) and B2 (CsCl) phases are studied theoretically with an improved electron gas model. The model incorporates the effect of crystal stabilization of the ionic charge densities by way of a Watson sphere-type potential. A series of such calculations as a function of sphere radius is performed to obtain the wave functions of the ions as a function of lattice constant and to obtain the volume dependence of the ion self energy. The latter is shown to make an important contribution to the equation of state. Elastic constants and phonons are calculated in the rigid ion quasi-harmonic approximation. From the effects of compression on the elastic constants and lattice dynamics, mechanical instabilities in both the B1 and B2 phases are identified. The quasi-harmonic frequencies are used to calculate the vibrational free energy and pressure contribution to the equation of state. The calculated (parameter-free) equations of state are found to be in good agreement with the available experimental data for both NaF and NaCl, including the pressure dependence of the thermal expansivity of the B1 phases and recent measurements of the room-temperature compression curves of the B2 phases. The B1-B2 phase transition is examined in detail, and comparisons with experimental and previous theoretical studies are discussed.