Free vibrations of coil springs are investigated as those of three dimensionally curved slender beams which form coil springs with constant pitch angle. Vibrations of coil springs, it has become clear, can be regarded as longitudinal vibrations of straight bars only in cases the pitch angle is very small, the ratio to the radius of wire and coil is small, and the spring has many numbers of turn. Morever, we introduced the exact frequency equations and modes as the vibrations of circular rings in the same manner as Waltking.