A method is described for specifying the transverse leakage (buckling) in each energy group of a multigroup solution of the neutron transport equation. For two dimensional geometry a transverse buckling is associated with one direction and the resulting one-dimensional problem is solved; this gives the first estimate of the energy dependent buckling in the first direction. The next calculation uses this energy dependent buckling as the transverse buckling for a one-dimensional calculation in the other direction. As applied to a completely reflected finite cylindrical core, the method uses the core absorptions and leakages obtained from a one-dimensional multi-group calculation to predict the group bucklings to be used in the next iteration in the other direction. The process is repeated until the buckling in each group in each direction converges. The IBM-704 multigroup diffusion code GNU has been used in conjunction with this buckling iteration method to compute the equivalent spherical radii of a number of fully reflected finite cylindrical cores for which experimental data are available. The equivalent sphere diameters as calculated by the buckling iteration method deviate from the experimental diameters by an average of two per cent over the range of core height to diameter ratios from ⅓ to 5. The converged value of the multiplication constant was found to be independent of the initial guess made for the axial or radial buckling and insensitive to the transverse bucklings assumed for the regions outside the core for all except very small cores.