Uranium-rich U-Zr alloys such as U-10Zr have been used in previous fast reactor experiments and are materials of interest for future fast reactor designs due to their high fissile density, favorable thermal properties, and ability to operate at higher burnups than traditional oxide fuels. A necessary step in validating U-10Zr and other U-Zr alloys for use in these future reactor designs involves understanding how the properties of the alloys change throughout their operational life-times. This includes the effects of thermal and mechanical stresses, as well as effects produced by the accumulation of radiation damage. Radiation damage events produce displacement cascades that result in the formation of many defects, some of which will anneal over a short time period, while others will remain in the lattice. Vacancy formation energies (VFE) play a significant role in simulations of radiation damage events, due to the impact of monovacancies on the diffusion of defects that were formed during the damage event. The VFE of body-centered-cubic uranium-zirconium alloys was calculated by two methods. In one case, atomistic configurations of a random U-Zr solid solution were generated, an atom was removed, and the vacancy formation energy was calculated. In the other case, the U-Zr solid solution was represented by a series of special quasirandom structures (SQS), before creating the defect and calculating the vacancy formation energy. The impact of nearest neighbor configurations on VFE for U-10Zr alloy was also examined. The molecular dynamics simulation code Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) was used to examine the differences in vacancy formation energies calculated for random structures produced by LAMMPS and SQS generated by the "mcsqs" code of the Alloy Theoretic Automated Toolkit (ATAT). Results indicate that there is not a statistically significant difference in the vacancy formation energies of alloys produced by random atom placement and alloys generated as SQS. Examination of the impact of nearest neighbor configurations on vacancy formation energy in the U-10Zr alloy showed that the vacancy formation energy did not vary significantly for configurations that were statistically likely to form in a random alloy. As the Zr concentration in the bcc solid solutions increases, vacancy formation energy for zirconium removal increases until a maximum value is reached around 50% Zr, then decreases to a value very close to the initial value. For uranium removal, vacancy formation energy initially decreases as the percent of Zr increases from 10%, reaching a minimum around 60 or 70% Zr, then increasing towards the uranium VFE in pure bcc uranium. These results can be used to parameterize higher length scale models of radiation damage and microstructural evolution of metallic U-Zr nuclear fuel.