The natural frequencies of helical springs having arbitrary shapes, such as conical, barrel and hyperboloidal, are obtained by the transfer matrix method using the distributed mass model and Timoshenko's beam theory together with the axial deformation. The governing equations of cylindrical helical springs are applied to free vibration analysis of non-cylindrical helices. It is shown that the present numerical results agree well with the previously published ones which have been obtained both theoretically and experimentally. A comparison of natural frequencies of non-cylindrical helices is made. For the circular section, the effects of the helix pitch angle, the number of active turns, the ratio of diameters of the minimum cylinder to the maximum cylinder, and the ratio of diameters of maximum cylinder to the diameter of wire on the free vibration frequencies of all types of helices are investigated. The effects of axial and shear deformations, and the rotary inertia are also studied. (C) 1997 Academic Press Limited.