The effect of 6H-SiC crystal growth shapes on the thermo-elastic stress distribution in the growing crystal was systematically investigated by using a finite element method. The thermo-elastic stress distribution in the crystal with a flat growth shape was more homogeneous than that in the crystals with concave and convex growth shapes, and the value of thermo-elasticity in the crystal with a flat growth shape was also smaller than that in the two other types of crystals. The maximum values of thermo-elastic stress appeared at interfaces between the crystal and the graphite lid. If the lid was of the same properties as 6H-SiC, the thermo-elastic stress would decrease in two orders of magnitude. Thus, to grow 6H-SiC single crystals of high quality, a transition layer of SiC formed by deposition or reaction is suggested; meanwhile the thermal field in the growth chamber should be adjusted to maintain the crystals with flat growth shapes.