The lateral vibration of an elastic bar, supported at two arbitrary :points is analysed and calculating the natural frequency, its characteristic variation and the nature of the extreme values that appedr during the transferring of the supports are made clear. As for the extreme values there exists a general rule which holds for all kinds of supporting conditions or any distribution of the cross section and the mass of the bar. But in this paper, the meaning and reality of this general rule are shown partially by the concrete analysis of the subject, leaving the more complete description of the rule to another study.