The non-linear analytic-numerically computed calculations with use of two different heat source models are adopted for Pulsed Power Welding (PPW). The following heat source models are used in this study: cylindrical-involution-normal (C-I-N) and double-ellipsoidal (D-E). At first the temperature fields generated by C-I-N and D-E heat sources with pulsed power in both stationary and moving co-ordinates systems (Fourier transformation form) are established.