A chucking device of the present invention includes an annular elastic member sandwiched between an upper and a lower member. A rod is slidable up and down in a bore formed in the upper and lower members and is partly positioned in the elastic member. The rod presses the elastic member radially outward when raised or lowered, thereby causing the chucking device to chuck a hollow, cylindrical base. The elastic member contacts the inner periphery of the base over a minimum of area and surely, closely contacts it for thereby implementing desirable sealing. The chucking device can therefore form a uniform film on the outer periphery of the base.