Quantum mechanical optical potential methods for calculating inclusive isotope and element production cross sections from the fragmenting of heavy nuclei by intermediate-and high-energy protons and heavy ions are presented based upon a modified abrasion–ablation-FSI (frictional spectator interaction) collision model. The abrasion stage is treated as a quantum mechanical knockout process that leaves the residual prefragment in an excited state. Prefragment excitation energies are estimated using a combined liquid drop and FSI method. In ablation the prefragment deexcites by particle and photon emission to produce the final fragment. Contributions from electromagnetic dissociation to single nucleon removal cross sections are incorporated using a Weiszacker–Williams theory that includes electric dipole and electric quadrupole interactions. Estimates of elemental and isotopic production cross sections are in good agreement with published cross section measurements for a variety of projectile-target-beam energy combinations.