This work is devoted to the computational modeling of a lightning strike electric arc discharge induced air plasma and the material response under the lightning strike impact. The simulation of the lightning arc plasma has been performed with Finite element analysis in COMSOL Multiphysics. The plasma is regarded as a continuous medium of a thermally and electrically conductive fluid. The electrode mediums, namely the cathode and anode, have also been included in the simulation in a unified manner, meaning that the plasma and electrode domains are simulated concurrently in one numerical model. The aim is to predict the lightning current density, and the heat flux impinged into the anode's material surface, as well as the lightning arc expansion and pressure and velocity of the plasma flow. Our predictions have been validated by the existing experimental data and other numerical predictions reported by former authors.