An analytical inactivation cross section formula based on the analytical formula for calculating the radial dose distribution of Awad et al. (Awad et al., 2018) was proposed. The formula is a multi-hit model based on the track structure theory of Katz that was not updated since Katz and co-workers in 1970s-1980s. The formula was solved numerically to calculation the inactivation cross section, σ and action cross section for double strand break, σ DSB for the two strains of the vegetative E. coli cells (B S-1 and B/r) bombarded with heavy ions of O, Ne, Ar, Kr, Xe, Au, Pb and U of energy between 1.1 to 19.4 MeV/n. The response of the cell and hence the corresponding inactivation cross section is affected by m, the number oftargets that must be inactivated per cell; D 0 , the characteristic x or γ-ray dose; a 0 , the target radius and R max , the maximum range travelled by the liberated δ-ray in the medium. The variations in the inactivation cross section in terms of these parameters were studied. The model predicts the available measured inactivation cross sections data for E. coli cells (B S-1 and B/r), σ as well as the double strand break, σ DSB ones with good accuracy. It was found that as the ion charge increases as the inactivation probability increases and the corresponding inactivation cross section of the ion increases.