Plasmas generated by electrical discharges at atmospheric pressure have lately been tested as new tools for acting on flows. Experimental results confirm that this type of electroaerodynamic triggers can effectively contribute to the modification of moving fluid properties. The operating modes of electrical discharges as well as the phenomena which contribute to such a result are poorly understood though. Large discrepancies are seen according to the type of discharge which is used, suggesting that the mechanisms of action are not yet identified. The present work is a theoretical study based on the numerical simulation of the steady state behavior of a crown discharge in pure air at atmospheric pressure. The mathematical model is composed of the laminar flow equations (mass and momentum conservation) and the Poisson equation for the computation of the electrical potential. The influence of the electrical field on the flow is taken into account by the addition of the electrical force term in the Navier Stokes equations. The validation of the model is based on experimental observations. The variation of dynamic, geometrical and electrical parameters is also studied. Fluent 6.3 software is used to perform numerical computations.