The presence of a large, sharp resonance at 1 ev in Pu240 results in the effective pile cross section for this isotope being very much larger than the true thermal cross section. Furthermore, the narrowness of this resonance causes the absorption of epithermal neutrons in Pu240 to be strongly self-shielded. Consequently, the effective cross section of Pu240 will be a function of reactor spectrum and of the Pu240 concentration at any given time. The significance of this effect can be appreciated by noting that the effective cross section of this isotope is frequently more than twice the effective thermal value. An approximate method of calculation has been applied to long term reactivity problems. The importance of the resonance augmentation and concentration dependence of the Pu240 cross section is particularly evident in the first few thousand Mwd/t and causes significant changes in the reactivity required to reach any longer burnout. Sample calculations are presented and comparisons with the Canadian experimental determinations of the effective Pu240 cross section are made. An effective constant Pu240 cross section is presented which will yield approximately correct burnout results when used in conventional irradiation studies.