The new approach for calculating neutron self-shielding factors taking into account isotropic multiple scattering, recently developed for the thermal region, is extended to epithermal resonance energies. The method is based on a collision function determined solely by the cross sections and the geometry of the probe submitted to the neutron field. The influence of the external field is separately included in the first collision probability distribution. Some advantages of the method with respect to the transport theory are discussed. Numerical results for the main epithermal resonances in cobalt and gold are presented, including the self-shielding factor as a function of the incident neutron energy.