It is quite customary to use a beam with different types of cross section or even structural discontinuities such as notch or crack along its span. Furthermore, in many occasions such beams may happen to be excited by outsider oscillatory fluctuations. So the study of their natural frequencies is important. In this regard, here the problem of frequency analysis of a discontinuous beam located an elastic foundation is studied. Vertical vibrations of a train or a ship may be considered as the typical examples of these vibrations. So herein the influence of different factors upon the natural frequency of a cracked and stepped beam located on an elastic foundation is assessed. To this ends, following the description of Timoshenko beam, wave method and a special trend used for the root finding of the frequency equation, a through analysis of natural frequency for different problems are represented. In some typical cases the validation of the results are assessed.

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