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[en] We have investigated the feasibility of using compound materials as targets for muon production by virtue of simulations using a GEANT4 toolkit. A graphite material and two thermostable compound materials, beryllium oxide (BeO) and boron carbide (B4C), were considered as muon production targets, and their muon production rates for a 600-MeV proton beam were calculated and compared. For the thermal analysis, the total heat deposited on the targets by the proton beams and the secondary particles was calculated with the MCNPX code; then, the temperature distribution of target was derived from the calculated heat by using the ANSYS code with consideration of heat transfer mechanisms such as thermal conduction and thermal radiation. In addition, we have investigated whether the heavy-ion beams can be utilized for muon production. For various beam species such as 3He2, 4He, 7Li, 10B and 12C, their muon production rates were calculated and compared with the rates experimentally-obtained for a proton beam.