Though a lot of researches on boundary layers around a moving body have been conducted, not only details of growing process of vortices but also relation between moving wall and vortices in the boundary layers are not clarified. In this study, the growing process of vortices near moving wall is explored numerically in case of heaving and elastic thin airfoil during one cycle Re=4,000 and St=0.36. As a result, the followings have been clarified in comparison between the rigid and elastic thin airfoils. The vorticity Z and -∂u/∂y have similar time development profile during one cycle at each location of the chord though these increase toward the trailing edge exclusive of the trailing edge. The vorticity Z near the wall is dominated by -∂u/∂y.