The objective of this book is to show the effect of flexible arm studied by dynamic analysis of a robot manipulator with two flexible arms. The book has been established for the undergraduate upper-levels and graduate level in Mechanical Engineering. Clearly, it is desirable to build lightweight robot arms which have a large working volume, high mobility and the capability to carry heavy payloads. In order to meet these requirements, the robot arm has to be flexible, in other words, the rigid-body-assumption in robotics has to be abandoned. Then, the deflection and vibration of the robot arm present a severe problem to the accuracy and the stability in positioning. Therefore, the control of flexible manipulators is becoming a critical issue in robotics. Modal analysis can improve physical knowledge of a structure and in some cases give us much information about its behaviour during operating. The calculation of the natural frequencies of the structure by modal analysis becomes today an important step in its design.