Quantification of rehabilitation progress is necessary for accurately assessing clinical treatments. A three-dimension (3D) upper extremity (UE) kinematic model was developed to obtain joint angles of the trunk, shoulder and elbow using a Vicon motion analysis system. Strict evaluation confirmed the system's accuracy and precision. As an example of application, the model was used to evaluate the upper extremity movement of eight hemiparetic stroke patients with spasticity, while completing a set of reaching tasks. Main outcome measures include kinematic variables of movement time, range of motion, peak angular velocity, and percentage of reach where peak velocity occurs. The model computed motion patterns in the affected and unaffected arms. The unaffected arm showed a larger range of motion and higher angular velocity than the affected arm. Frequency analysis (power spectrum) demonstrated lower frequency content for elbow angle and angular velocity in the affected limb when compared to the unaffected limb. The model can accurately quantify UE arm motion, which may aid in the assessment and planning of stroke rehabilitation, and help to shorten recovery time.