Calculations are presented of the thermal-neutron flux as a function of position in a water moderator surrounding a variety of thick targets which are bombarded by protons in the energy range 540 to 2000 MeV. The calculated results are compared with experimental values, and very good agreement is obtained. Results are also given for the thermal-neutron flux as a function of position in a D2O moderator and for the energy deposition in the targets and the moderators.