This article describes methods for the computer aided design of electron and ion beam columns for the integrated circuit (IC) manufacturing industry. The techniques described include computation of field distributions in electron lenses and deflectors, electron trajectories and aberrations, dynamic corrections, effects of discrete Coulomb interactions, design of electron guns, treatment of diffraction effects, optimization, and tolerancing of complete columns. These techniques are illustrated with examples relevant to the IC manufacturing industry, including systems for high-throughput electron beam lithography, nanolithography systems, and electron beam systems for inspection, metrology, and voltage testing.