In this study, out of plane vibration characteristics of curved beams having variable curvatures and cross-sections are studied by FDM (Finite Difference Method). The effects of curvature and cross-section of the curved beam on natural frequencies are investigated for the curved beams having; variable curvature & constant cross-section and variable curvature & variable cross-section. Mathematical model of the present problem is based on the coupled differential eigenvalue problem with variable coefficients. Numerical solutions of the problem in this study are obtained by the computer program developed in Mathematica. The accuracy of the present results obtained from the developed program is evaluated by comparing with FEM (Finite Element Method) results found from solid model created in ANSYS. Good agreement is obtained in the comparisons of the present results with other results. All results are presented in tabular and graphical forms.