Abstract: A non-singular single integral mathematical model is applied to calculate the external longitudinal magnetic field induced by a single axisymmetrical and cylindrical hollow coil and used for CO₂ arc welding.And the coil is coaxial to electrode and excited by a revisably pulsed current of square wave.The means is very easy,quick and has high precision.We also compare the calculated result to the metrical result.The result shows that the numerical simulation model is accurate、reliable and effective.