Abstract: In the present study, the transient approximate formulas for ELF electromagnetic field excited by a double exponential function are derived due to a vertical electric dipole on the ground at near distances representing a lightning discharge process. The approximate solution is obtained from simplifying the Sommerfeld’s integrals with the quasi-static approximation. The computational scheme, simulating the characteristics of time- and frequency-responses for ELF wave representing the lightning pulse signals, exploits the results of an approximate unit impulse response from frequency domain and convolution of which with a double exponential exciting function, and provides with the analytical transient expression of the ELF waves from the inverse-Fourier-transformation. The study illustrates a simple but effective estimation for the lightning pulses in the near region in the application of electromagnetic compatibility systems.