In this work, a physical model for Laser Induced Breakdown in air for combustion applications is proposed. Inverse Bremsstrahlung, air breakdown chemistry and shock dynamics are taken into account. The air plasma is modeled via the Navier-Stokes equations, where non-equilibrium effects are described by means of a two-temperature model. The flow governing equations are coupled to the radiative transfer equation (i.e., Kinetic Theory of photons) to account for laser-plasma interactions. The two sets of governing equations are solved using the FIN-S framework, where the Navier-Stokes equations are discretized based on an SUPG Finite Element Method. The discretization of the radiative transfer problem is accomplished via a Finite Volume method. Simulations are performed to predict the plasma evolution during breakdown and post-breakdown stages. A comparison between the computed and experimentally determined shock diameter is also reported, showing a good agreement between the two predictions.