We study integrals that arise in the calculation of electric multipole moments. A computational approach is developed to evaluate these integrals in an STO basis set in a straightforward, yet somewhat untraditional fashion. The computation involves a simple three-step procedure: translation of all Cartesian parts to one center, local evaluation, and a single one-sided rotation into the molecular frame. Some assessment on this method is discussed. An implementation of the method is presented in this paper to compute overlap, dipole, quadrupole, octopole, and hexadecapole moment integrals in a basis set that includes up to g orbitals. © 1993 John Wiley & Sons, Inc.