The binary-encounter-Bethe (BEB) model for calculating electron-impact ionization cross sections for molecules is described with emphasis on polyatomic molecules and their radicals and ions. The BEB model provides an analytic formula for the cross section. The formula is for each molecular orbital, and requires only three numbers from the initial state of the target molecule: the electron occupation number, the orbital binding energy, and the orbital kinetic energy. The sum of the orbital cross sections provides the molecular cross section. The BEB model produces reliable ionization cross sections from the threshold to several keV in incident electron energy for neutral molecules and ions. The BEB cross sections for some fluorine-containing radicals are almost a factor of two larger than available experimental values. Molecular constants are included to generate BEB cross sections forH2,C2F6,H2+,CH3,CFx,BFx,BClxforx=1–3,and several unsaturted molecules relevant to hydrocarbon combustion. ©2000 American Institute of Physics.