Functional impairments of the Upper Extremity (UE) are common not only among the elderlies, but can also result from cerebrovascular accident (CVA), amyotrophic lateral sclerosis (ALS) and spinal cord injury (SCI) in any individual. Citing the constant growth of UE Dysfunctions and required prolonged rehabilitation, robot-assisted therapy has already been contributing to restoring UE functions. Though, extensive research has been conducted on rehabilitation robotics, limitations still exist compared to required degrees of freedom and range of motion for effective UE rehabilitation. In this research, we have developed a 3-DOF robotic exoskeleton to provide rehabilitation therapy to the shoulder and elbow joints. The exoskeleton was designed for typical adult; provision includes for link-length adjustment to accommodate a wide range of users. The robot arm will be attached to the lateral side of human UE to provide shoulder joint vertical and horizontal flexion/extension and elbow flexion/extension motion. Modified Denavit-Hartenberg notions were used to develop the kinematic model and Newton-Euler formulation was used for the dynamic modeling of the developed robot. Control has been implemented on LABVIEW environment. Experimental results revealed that this robot can be effectively maneuvered to follow the desired trajectories (shoulder and elbow joint motion) to provide passive rehabilitation therapies.