A graphite target system to produce rare isotope beams using in-flight fragmentation method has been designed for the rare isotope science project in Korea. A main primary beam to bombard the target is 238U in the energy of 200MeV/u with a maximum power of 400kW, in which the beam power deposit on the target amounts up to 100kW. A multi-slice target concept was adopted to enhance radiation cooling effect. A finite element program ANSYS was used to analyze thermo-mechanical behavior of a single and multi-slice targets. To validate the design, an electron beam at the energy of 50keV was used to test a single slice target. A good agreement of the hot spot temperature was achieved between the simulation and measurement. For multi-slice targets a series of ANSYS analysis was performed in search of the optimal design. Target design parameters for the isotope beam production, which can sustain an incident 400-kW 238U beam, have been found.