Abstract: For multi-region co-centre cylinder cell the numaricll solution of neutron moderating integral equation is a approximate solution using Lobatto quatrature formula. It can get more accurate epithermal energy spectrum, therefore resonance integral, group cross-section and self-shielding factor of resonance as well.Using the method of step by step recurrece to calculate moderating souece and the premade table of P_ij to interpolate collision probability, a great deal of computing time could be saved. In this paper resonance cross-section for ²³⁵U, ²³⁹Pu were calculated using multi-level formula so as to consider interference and overlap ping effect between resonances.A check calculation has been made based on the model provided by Ref.^[7]and the both results agree well eath other.