Exoskeleton Robot is one of the most significant examples of human-oriented robotic devices. Nevertheless, the main challenge remains the complexity of their mechanical design and human-robot interfaces. This paper is an outcome of a research to model and to simulate the support of mobility of an elderly people using exoskeleton. Exoskeleton is developed in order to complement the corporal deficiencies of an elderly person in standing up and sitting down. When the natural joint torques is integrated with the exoskeleton's torque the result is in an overall torque that is comparable to that of a physically normal person. This work focuses on standing-up and sitting-down movements. Appropriate simulation models are formulated and their performances examined against measured data. The results with PID control show that at different speed of standing up and sitting down, the joint torques can be compromised. This is done within allowable limits.