Optimum cross sections of cylindrically coiled spring are analyzed by the growth-strain method. This method was previously proposed as a shape optimization method which deforms shapes by generating bulk strain. In the present analyses, the helix angle is neglected. The stress distributions are analyzed by the finite element method based on the stress function. The growth deformation is analyzed by the finite element method on the assumption of a roll of coil as a rotationally symmetric ring under free restriction. The bulk strain is generated based on the strain energy density in a manner in which volume change in the cross section is absorbed in the circuit direction. In consequence, a convergent curve of mass improvement ratio and corresponding cross sections are obtained. The cross sections are egg-shaped tapering to the outside of the coil.