Abstract: The weveform distortion of γ-ray pulses propagating in the atmosphers is dealt with in terms of the combination of Monte-Carlo method and the fold integration method.Mathematical expressions are given for the propagation function of γ-ray with any energy spectrum distributions in the atmosphere and the fold integration calculation of γ-ray pulse waveforms at detection points.The effects of γ-ray propagating on the waveforms have been calculated for some typical pulse waveforms.Discussion covers the treatment to decrease or avoid waveform distortion.

Key words: Pulsed γ-ray, propagation function, scattering function, fold integrating, waveform distortion