Industrial robots are used for supplying an automatic machine with some kinds of partsor for loading and unloading the works to the machine. In these cases, the robot arm movesintermittently. When the robot arm is driven at a high speed, positioning error at the settlement place (the cam-dwell mode) is generally drawn because of the residual vibration whichis caused for the lack of stiffness. This paper deals with a method of reducing a residualvibration rapidly. It is realized by inserting a spring-mass-damper system between the driving system and the robot arm. Here, we define the optimal parameters on the combinationof a spring, a damper, and a mass for the elastic support which has the steepest slope of theenvelope curve of the residual damped vibration. After an analysis, the optimal parametersare given by β=1 and ζd=1/√α. Where, β; ratio of the undamped natural frequencies of theelastic support and the robot arm, α; ratio of the masses of the elastic support and the robotarm, and ζd; damping ratio of the elastic support. Two practical examples of the elasticsupport are shown. One is a high speed positioning system of a robot arm driven by anindexing-cam mechanism and the other is the system of a robot arm driven by a pneumaticactuator.