An apparatus for producing SiC single crystals where the quality of the SiC single crystals is improved, and a production method using such an apparatus are provided. The apparatus for producing SiC single crystals according to an embodiment of the present invention is employed to produce an SiC single crystal by the solution growth method. The production apparatus includes a crucible and a support shaft. The crucible accommodates an Si—C solution. The support shaft supports the crucible. The support shaft includes a heat removing portion for removing heat from a bottom portion of the crucible. The heat removing portion includes one of (a) a contact portion having a thermal conductivity not less than that of the bottom portion and contacting at least a portion of the bottom portion and (b) a space adjacent to at least a portion of the contact portion or the bottom portion.