We present a theoretical investigation of plasma generation in sodium vapor induced by laser radiation tuned to the first resonance line (3S-3P) at λ = 589 ns. A set of rate equations that describe the rate of change of the ground and excited states population as well as the temporal variation of the electron energy distribution function (EEDF), beside the formed atomic ion Na+, molecular ion  and tri-atomic ions are solved numerically. The calculations are carried out at different laser energy and different sodium atomic vapor densities under the experimental conditions of Tapalian and Smith (1993) to test the existence of the formed tri-atomic ions. The numerical calculations of the electron energy distribution function (EEDF) show that a deviation from the Maxwellian distribution due to the super elastic collisions effect. In addition to the competition between associative ionization (3P-3P), associative ionization (3P-3D) and Molnar-Horn- beck ionization processes for producing , the calculations have also shown that the atomic ions Na+ are formed through the Penning ionization and photoionization processes. These results are found to be consistent with the experimental observations.