The main purpose of this paper is to present both the fundamental frequency and some higher free vibration frequencies for the cantilevered arcs with the variable cross-section. The linearly varying moment of inertia of cross-section for the variable cross-section is choosed, and the three kinds of the sectional shape of the rectangular cross-section are considered in numerical analysis. As the numerical results, the four lowest natural frequencies are presented as functions of the nondimensional system parameters : the section ratio, the slenderness ratio, and the subtended angle. The effect of rotatory inertia on the natural frequencies is reported. In addition, the typical mode shapes of the displacements and stress resultants are presented in figures.