The objective of this study is to develop a technique for the quantitative evaluation of spasticity in the upper limbs. The subjects were two healthy volunteers and 19 hemiplegic patients. Each subject was seated or standing in a resting state, and the forearm was flexed five times and extended five times in each posture through a force-and-torque sensor placed on the wrist. The forearms of subjects who could not stand up were flexed and extended only in a seated position. The elbow joint angle, torque, and electromyograms (EMGs) of the biceps brachii muscle, triceps brachii muscle, and brachioradialis muscle during flexion and extension were measured. The inertia of forearms and visco-elastic coefficients were estimated by the least squares method with a mathematical model that consisted of elastic components depending on the elbow joint angle and muscle activities. The elbow joint angle and torque were then estimated with the obtained inertia and visco-elastic coefficients and compared to the observed angle and torque in order to evaluate the performance of the mathematical model. The elbow joint angle and torque were closely estimated by the mathematical model. Next, the maximum value of the elastic coefficient during flexion/ extension around the elbow joint (kmax) was calculated and compared with the Ashworth scale. The results show that the kmax had a tendency to increase as the Ashworth scale increased. In conclusion, the mathematical model could represent the relationship between the elbow joint angle and torque. The kmax would be medically and clinically useful for the quantitative evaluation of spasticity in hemiplegic patients.