Upper extremity stiffness is a biomechanical parameter with implications for rehabilitation engineering, human operator dynamics and robotics. It is also a multidisciplinary topic, relying on digital signal processing and inverse kinematics. This thesis examines three numerical inverse kinematics solution techniques as applied a robotic end effector and human upper extremity. A method for measuring limb stiffness in the frequency domain using a seven-axis robot and digital signal processing techniques is also outlined. Through simulation, it was verified that the BFGS algorithm is preferable for situations with high initial estimate error, while the NR and LM methods are superior when minimizing computing cost is a priority as in real-time applications such as human controlled robots in rehabilitation engineering. Synthetic limb stiffness data was found to produce plots similar to those found in other research, however, the collection frequency of experimental data was too low to capture the full frequency range needed for dynamic modeling