Drillstring instability phenomena leads to damage all parts of the drillstring, wellbore instability and reducing the rate of penetration (ROP). The bottom hole assembly (BHA) configuration is a main factor in optimizing the drilling operations. Therefore, should be designed to minimize the vibration levels in the lateral, axial and torsional directions. This can be done, by avoiding the rotation of the drillstring at the natural frequency which called the resonance. In this thesis the vibration of drillstring was studied under the impact of weight on bit and rotation drillstring. Thus, the lateral vibration has been chosen as the most important and centered element, because it is increased dramatically with the variation of the rotary drilling speed.