We have performed two experiments in the fast critical assembly BFS to measure the effective delayed neutron fraction $eta$$_{eff}$ values and compared the results to validate the $eta$$_{eff}$ computation code, BETA-K. Measurements of $eta$$_{eff}$ were carried out in a metallic plutonium core and a metallic uranium core with Cf$^{252}$ source pseudo-reactivity method. Fission integrals and correction factors, which were used to obtain the experimental $eta$$_{eff}$ values, were calculated by using the LMR core design computation code system of KAERI. BETA-K has been developed consistently with the hexagonal Nodal Expansion Method (NEM) and it used delayed neutron data of ENDF/B-VI. By comparing the computed $eta$$_{eff}$ values with the measured ones, we found that the results from BETA-K agreed with the experimental values within the experimental error bound.ror bound.