At the present thesis,a position control of an elastic robot arm of one DOF is performed. An elastic joint has been chosen from the robot KUKA LWR-4. The purpose of this report is the modeling and the position control of the elastic joint. Initially the real joint is examined, the parts of the joint are analysed and all the parameterswhich are used for the mathematical description of the joint are set.We make some assumptions (eg linear model) and the system in which we will make the position control is designed. The existence of elasticity in the model is described with the addition of atorsional springand a viscous damping. With the help of Newton’s and Kirchhoff’s law, the equations which describe the examined system are defined. Subsequently theory is stated and we propose methodologies of controlling the system. Initially we use a P and afterwards a PD-Controller, a root-locus analysis is done, the stability of the system is tested, we examine the Ziegler-Nichols method and at last we analyse the system in state-space and a full-state feedback control is made. Thereafter the various approaches of controlling the joint are analysed, the methodologies are examined and the results are presented. As it is going to be noticed, one of the biggest issues in position control of the elastic joint is the existence of oscillation, due to elasticity.In conclusion, we examine the results and we compare the methodologies, in order to investigate which is the best methodology.