The stability of the shapes of crystal growth face and dissolution face in a two-dimensional mathematical model of crystal growth from solution under microgravity is studied. It is proved that the stable shapes of crystal growth face and dissolution face do exist, which are suitably shaped curves with their upper parts inclined backward properly.The stable shapes of crystal growth faces and dissolution faces are calculated for various values of parameters, Ra, Pr and Sc. It is shown that the stronger the convection relative to the diffusion in solution is, the more backward the upperparts of the stable crystal growth face and dissolution face are inclined. The orientation and the shape of dissolution face hardly affect the stable shape of crystal growth face and vice versa.