Abstract The model of Cengiz (2002) [Approximate inelastic scattering cross sections of electrons. Rad. Phys. Chem. 65, 33–44] has been modified by incorporating both the ionic and relativistic corrections due to Uddin et al. (2006) [Modified Kolbensvedt model for the electron impact K-shell ionization cross-sections of atoms and ions. Eur. Phys. J. D 37, 361–369.] to investigate the electron impact s-orbital ionization in the K- and L-shells. With a single set of species independent parameters our evaluated inner shell ionization cross section of atomic targets from H to U over incident energies up to 2GeV and of H- to Be-isoelectronic series reproduce the experimental findings nicely.