Methods for calculating wavefunctions and eigenvalues of image potential states are presented. We consider cases corresponding to metal-vacuum interfaces, metal-dielectric medium interfaces and metal-dielectric medium-vacuum interfaces. We represent the metal as a perfect conductor or as a Fermi-Thomas metal. We present the dependence of the wavefunctions and eigenvalues of the image potential states on dielectric constants, electron affinity, work function of the metal, and inverse Fermi screening parameter. (C) 2001 American Institute of Physics.