A new method of calculation is presented for directional probabilities of interaction in pin clusters and rod lattices. The theory, in principle rigorous from a geometrical point of view, has been programmed for the IBM-7090 as the computer code PROCOPE. Calculation results for Dancoff correction factors and collision probabilities are compared with values obtained with other methods. The validity of the technique is also checked by evaluating the fine structure of the thermal flux distributions in various gas-cooled clusters upon which measurements have been made at Saclay. As a practical illustration, a series of curves describes the behavior of the various independent fuel-to-fuel collision probabilities in 19−(or 7−) pin gas-cooled clusters. Finally, approximate formulas are given for the pin-to-pin collision probability at both the white and the black limits.