Method of producing sic single crystal

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A method of producing a SiC single crystal includes : disposing a SiC seed crystal at a bottom part inside a graphite crucible; causing a solution containing Si, C and R (R is at least one selected from the rare earth elements inclusive of Sc and Y) or X (X is at least one selected from the group consisting of Al, Ge, Sn, and transition metals exclusive of Sc and Y) to be present in the crucible; supercooling the solution so as to cause the SiC single crystal to grow on the seed crystal; and adding powdery or granular Si and/or SiC raw material to the solution from above the graphite crucible while keeping the growth of the SiC single crystal.