A Monte Carlo code is used to calculate the fast effect in both homogeneous and heterogeneous systems. The following results are obtained: for an infinite block of natural uranium, δ28 = 0.39, ∈ = 1.247; for an infinite block of beryllium, ∈ = 1.078; for beryllium oxide, ∈ = 1.046. In addition, results are given for homogeneous mixtures of uranium and beryllium. Calculations have also been carried out for uranium-water lattices and compared with experimental results for slightly enriched uranium rods and slabs, and uranium oxide rods. Other results show the increase in ∈ when uranium fuel elements are surrounded by beryllium cladding of varying thickness.