Arcs in cross flow are encountered in a number of applications, for example in wire arc spraying. Optimization of such processes has relied in the past on an empirical approach and on intuition based on a qualitative understanding of the process. A theoretical treatment of an arc exposed to a cold gas flow perpendicular to its axis requires a three-dimensional (3D) formulation. A computer code has been developed to solve the 3D conservation equations for an atmospheric pressure argon arc in cross flow, and this code has been validated by comparison with previously published experimental results. Results have been obtained for typical conditions encountered in a wire arc spray situation, arc current 100 to 200 A, and arcing gaps of 1 and 2 mm, and varying cross-flow velocities. Results are presented in the form of temperature and velocity fields, and current density and potential distributions. It is apparent that the location of the highest temperature does not coincide with that of the highest electric power dissipation because of transverse convective effects, and that the anode attachment is farther downstream than the cathode attachment. The results clearly indicate that 3D modelling is required to capture the physical effects of the arc in cross flow, and that the code can be used to illustrate the parametric dependences of the plasma flow in various cross-flow situations.