A method for calculating the first-flight collision probabilities in an annular region containing identical cylindrical fuel rods is described. Based on the assumptions of flat isotropic neutron sources and isotropic incidence fluxes on boundary surfaces, 5 of the 15 probabilities in the annular region are calculated. By neutron conservation and the reciprocity theorem, the other 10 probabilities are obtained in terms of the first 5. The results are satisfactory in comparison to other existing theories. The method can be used in the treatment of a cluster-type fuel assembly.