Vertical displacement, critical Euler buckling load and vibration behavior of a cracked beam are considered in this research. The crack inside the beam is placed in different positions and results compared for each crack position. On first Eigenvalue of free vibration results, there is a border that first Eigenvalue of free vibration does not change if center of crack is located on that border, and after that border, the first Eigenvalue of free vibration is increased that is a counterexample relation of critical Euler buckling load and first Eigenvalue of free vibration.