Several reactor system components, such as heat exchange tubes, fuel fins, controlrods, and various instruments are beam-like components. This study presents a simple solution method for calculating the natural frequencies and modes of beams supported by linear and torsional springs and attached concentrated mass and rotational inertia at some intermediate points. For a general multi-span beam, theoretical method is proposed to analyze the exact solution about vibrational characteristics with respect to the nondimensional parameters. And the results obtained using the numerical models are presented and discussed.