Many reactor components including fuel assembly, heat exchanger tubes and control element assembly are typically beam-type structures with either classical or nonclassical boundary conditions, or both. In such cases, it is quite difficult to evaluate the vibration characteristics of the structures since methods for calculating accurate natural frequencies of those structures with complicated restraints are not generally available. In this study, the frequency equations for calculating the natural frequencies of the beams with generally restrained boundary conditions by both translational and rotational springs are derived in the matrix form using Fourier sine series. In order to show the validation of the solution, numerical results for two degenerate cases are compared with the existing results for natural frequency obtained by the conventional analysis. And as a specific application, the natural frequencies of fuel rod for Korean Standard Nuclear Plant (KSNP) fuel assembly are calculated and compared with the external excitations. As a result, the frequency equation derived by present paper seems to be very useful to evaluate the fuel rod vibration with various boundary conditions. Especially, when some parametric analyses are needed to modify fuel design, the equation can be applied very easily.