A method of calculating first-flight collision probabilities in cluster geometry is developed. The method is analytic and approximate and is comparable in speed to codes now available for annular geometry. The proposed scheme is based on a consideration of the properties of the nonescape probability from a nonuniform body in the limits of high and low macroscopic cross sections, together with an interpolation procedure that allows one to determine the probability itself with sufficient accuracy. When calculated for combinations of different rings of fuel pins in a cluster, the resulting set of nonescape probabilities enables one to proceed to a determination of the probability of going from one ring to another. The coolant and the fuel pins are treated separately. Results of the method are compared with exact calculations on two fuel-element types of current interest. In these cases the form factor, defined as the ratio of maximum to mean flux in the cluster, is in error by at most 2%. The hyperfine structure in each ring (i.e. the ratio of the mean flux in the coolant to the mean flux in the fuel) is calculated with comparable accuracy. A one-group calculation on a 37-rod fuel element takes approximately 5 sec on an IBM-7090, so that the method is certainly usable for multigroup applications.