The paper deals with the analysts of damping characteristics of a curved composite shaft. The composite shaft consists of an outer elastic curved tube with a similarly curved rod placed inside. The annular space between the tube and the rod is filled with viscoelastic material. The composite shaft is clamped at one end and a concentrated load (varying harmonically) acts on a radial arm fixed to the outer shell at the free end. It is shown that optimum design values exist for maximizing the total damping capacity of the system. It also is indicated that direct use of this method for increasing the damping capacity is not effective, as the damping factor reduces sharply after reaching a maximum value. It is shown how this difficulty can be overcome and how helical springs, possessing considerable damping capacity, can be designed. Sometimes this may help in simplifying the design of vibration isolators which will take the shape of a simple spring only.