Argonne National Laboratory (ANL) of the United States developed and designed a neutron source facility for Kharkov Institute of Physics and Technology (KIPT) of Ukraine. The facility was constructed at Kharkov, Ukraine and its commissioning process has been started. The facility has an electron accelerator driving a subcritical assembly. The electron beam power is 100 kW using 100 MeV electrons. The subcritical assembly has WWR-M2 fuel assemblies with U-235 enrichment of 19.7 wt%. The facility will be utilized to perform basic and applied nuclear research, to produce medical isotopes, and to train young nuclear specialists. Solid target design with stacked disks is selected and each target disk is cooled by water from both side. Tungsten or natural uranium is the target material. This paper presents the target design optimization to maximize the neutron yield and the neutron flux level of the facility while satisfying the thermal-hydraulic design criteria. Monte Carlo computer code MCNPX is utilized for the neutron yield analyses with ENDF/B-VII.0 nuclear data libraries, as a function of target thickness using a simplified target model without cladding or coolant channels. It's found that the neutron yield saturates at target thickness ~ 60 mm for both tungsten and uranium materials. For the final target design with cladding and coolant channels, the total uranium thickness is 56.5 mm, and the total tungsten thickness is only 33.0 mm. The tungsten material has a large absorption cross section for thermal neutrons. If the tungsten thickness is increased, the neutron yield gain is offset by the neutron absorption reaction. The paper presents the design optimization analyses for both target materials.