[en] The Japan Atomic Energy Research Institute (JAERI) is progressing design and R and D activities under the neutron science project with a high-intensity proton accelerator. JAERI has a plan to construct a neutron scattering facility with a neutron spallation source as the first neutron science facility, and is developing a target system as the neutron spallation source. This report presents preliminary estimation about a solid methane-liquefied hydrogen two-phase flow moderator that is the most promising thermal neutron moderator in a MW-class target. Temperature conditions in a solid methane particle and a moderator container, with a multiple structure were analyzed using a mathematical analysis software - MATHEMATICA. From the analytical results, it was found that, a center temperature of the particle less than 1mm in diameter could be maintained under 30K by far lower than the melting point of methane (90.7K) at about 20W/cm³ of a heat generation density in the solid methane. In order to prevent nucleate boiling on the inner surface of the moderator container, it is necessary to control liquid hydrogen temperature around 18K under the conditions of 3mm in thickness, 4m/s flow velocity and 3mm in helium gap. As the future work to solve engineering problems, it was pointed out key problems such as an optimization of the container structure from viewpoints of thermal and hydraulic performance to realize a disperse flow of methane particles as well as structural integrity. (author)