Recently, DS (Directionally Solidified) and SC (Single Crystal) alloys have been widely applied for gas turbine blades instead of CC (Conventionally Casting) alloys to meet the requirement of the high temperature operation and to improve the thermal efficiency. The SC blade consists of one columnar grain, and the DS blade consists of several columnar grains where the growing direction of the columnar crystal is set to the direction of the centrifugal force. Therefore, the vibration analysis of the SC and DS blades has to be carried out, taking account of the anisotropy. In this study, first, the effect of the anisotropy of elastic constants on the vibration characteristics of the SC and DS blades are investigated in detail. Second, the validity of the assumption of the transverse isotropy for the DS blade is examined, carrying out the Monte Carlo simulation. From these results, it is concluded that the actual DS blade can be treated as a transversely isotropic material.